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WORKING PAPER · NO. 2021-68

Could Vaccine Dose Stretching Reduce COVID-19 Deaths? Witold Więcek, Amrita Ahuja, Michael Kremer, Alexandre Simoes Gomes, Christopher M. Snyder, Alex Tabarrok, and Brandon Joel TanJUNE 2021

Could Vaccine Dose Stretching Reduce COVID-19 Deaths?Witold Wiecek, Amrita Ahuja, Michael Kremer, Alexandre Simoes Gomes,

Christopher M. Snyder, Alex Tabarrok, and Brandon Joel Tan

June 2021

Abstract: We argue that alternative COVID-19 vaccine dosing regimens could potentially dramat-ically accelerate global COVID-19 vaccination and reduce mortality, and that the costs of testingthese regimens are dwarfed by their potential benefits. We first use the high correlation betweenneutralizing antibody response and efficacy against disease (Khoury et. al. 2021) to show thathalf or even quarter doses of some vaccines generate immune responses associated with high vac-cine efficacy. We then use an SEIR model to estimate that under these efficacy levels, doublingor quadrupling the rate of vaccination by using alternative doses would dramatically reduce infec-tions and mortality. Since the correlation between immune response and efficacy may not be fullypredictive of efficacy with alternative doses, we then use the SEIR model to show that alternativedosing would substantially reduce infections and mortality over a wide range of plausible efficacylevels. Further immunogenicity studies for a range of vaccine and dose combinations could de-liver outcomes in weeks and could be conducted with a few hundred healthy volunteers. Nationalregulatory authorities could also decide to test efficacy of alternative dosing in the context of vacci-nation campaigns based on existing immune response data, as some did for delayed second doses.If efficacy turned out to be high, the approach could be implemented broadly, while if it turned outto be low, downside risk could be limited by administering full doses to those who had received al-ternative doses. The SEIR model also suggests that delaying second vaccine doses will likely havesubstantial mortality benefits for multiple, but not all, vaccine-variant combinations, underscoringthe importance of ongoing surveillance. Finally, we find that for countries choosing between ap-proved but lower efficacy vaccines available immediately and waiting for mRNA vaccines, usingimmediately available vaccines typically reduces mortality.

Keywords: vaccine, pandemic, epidemiology, public health, supply

Acknowledgments: The authors are grateful to Nora Szech, Ezekiel Emanuel, Marc Lipsitch,Prashant Yadav, Patrick Smith, Frédéric Y. Bois, Virginia Schmit, Victor Dzau, Valmik Ahuja,Marcella Alsan, Garth Strohbehn and seminar participants at Harvard, M.I.T., the University ofChicago, and the NBER Entrepreneurship and Innovation Policy and the Economy conference forhelpful comments and to Esha Chaudhuri for excellent research assistance.

Disclosures: This work was supported in part by the Wellspring Philanthropic Fund (Grant No:15104) and Open Philanthropy. Wiecek provides scientific consultancy for Certara, a drug devel-opment company and 1 Day Sooner, a COVID-19 human challenge trial advocacy group. Wiecekreports no material conflicts of interest with regards to development of COVID-19 vaccines.

Contact Information: Wiecek: Independent researcher <witold.wiecek@gmail.com>. Ahuja:Douglas B. Marshall Jr. Family Foundation <amrita.b.ahuja@gmail.com>. Kremer: Departmentof Economics, University of Chicago <kremermr@uchicago.edu>. Simoes Gomes: Departmentof Economics, University of Chicago <asimoes@uchicago.edu>. Snyder: Department of Eco-nomics, Dartmouth College <chris.snyder@dartmouth.edu>. Tabarrok: Economics Department,George Mason University <tabarrok@gmu.edu>. Tan: Economics Department, Harvard Univer-sity <btan@g.harvard.edu>.

1. Introduction

Most of the world is facing a shortage of COVID-19 vaccines, and it is unclear how much produc-

tion capacity can be added in time to materially affect the pandemic. In this paper, we investigate

the public health impacts of dose stretching policies to vaccinate people more rapidly. In particular,

we consider: (1) alternative doses, (2) longer delays between first and second doses, and (3) uti-

lizing available vaccines rather than waiting for higher efficacy ones. We first discuss available

evidence on the potential impact of such policies on protective efficacy for individuals receiving

vaccines and then combine this evidence with an epidemiological model to assess overall impacts

on public health. We find that vaccinating more people using dose stretching policies yields large

reductions in mortality and infections if efficacy remains high, and potentially even if such policies

entail considerable loss of efficacy.

For some dose stretching strategies, there is considerable evidence on efficacy from clinical

trials and real world data that can inform epidemiological modeling. For example, we can readily

examine the trade-offs that a country might face when choosing between a 70% effective vaccine

available immediately, and a 95% effective vaccine available in two months. Longer delays be-

tween first and second doses—i.e., "first doses first" (FDF)—which allow more people to get at

least one vaccine dose faster, have already been implemented by a number of countries. Clinical

and observational data suggests high first-dose efficacy for certain vaccines against some variants

of the virus, but lower efficacy for other vaccine-variant combinations.

There is no clinical evidence, to our knowledge, of the efficacy of alternative doses of COVID-

19 vaccines. Therefore, to estimate the potential efficacy of alternative dosing, we combine existing

data showing a high correlation between immune response and efficacy across vaccines (Khoury

1

et al. 2021) with early-stage clinical trial data on immune responses produced by different vaccine

doses. While sample sizes are low, the results suggest that lower doses may be highly effective. For

example, clinical trial data for mRNA-1273 (the vaccine developed by Moderna and manufactured

by Moderna and GC Pharma) suggests that half doses produce an immune response associated

with close to 95% efficacy, very similar to that of the standard dose. This evidence, while far from

dispositive, suggests that half (or even quarter) doses of some vaccines could plausibly provide

efficacy comparable to that of currently used doses.

We then use an SEIR model to assess the potential impact of dose stretching strategies when

the immunization rate is constrained by available supply. The immunization rate in our base case

scenario corresponds to the global vaccination rate as of early May 2021, which is roughly 0.25%

of the population per day.1 At this baseline speed, a 95% effective vaccine averts 18–50% of

infections compared to not vaccinating.2 Doubling the vaccination rate by moving to a half dose

of a COVID-19 vaccine averts 41–70% of infections if there is no loss in efficacy. Even if half

doses are only 70% effective, moving to a half dose and doubling the pace of vaccination would

substantially reduce infections and deaths relative to the status quo policy.

If first-dose efficacy is 80%, as suggested by UK data on BNT162b23 (the vaccine developed

by BioNTech/Pfizer and manufactured by Pfizer and Fosun Biotech), then FDF reduces mortality

by 29% and infections by 39% in a fast-growing epidemic scenario (R= 2) with vaccination speed

of 0.75% of the population per day. The magnitude of benefits depends on epidemic and baseline

1The number of doses administered daily per 100 people. See Mathieu et al. (2021).2The range of results correspond to the various scenarios simulated, ranging from a slowly decreasing epidemic

(effective R= 0.99) to a fast-growing epidemic (R= 2) peaking three to four months after the start of the simulation.Under the maintained assumption that high-risk groups are prioritized for vaccination, we find that faster vaccina-tion typically has more impact on preventing deaths than infections. We also vary model parameters to account foruncertainty about efficacy of alternative dosing and FDF.

3This includes efficacy against the variants prevailing in the UK in the early part of 2021.

2

speed, but even if efficacy in the period between the first dose and second dose is as low as 50%

(allowing time for immunity from the first dose to develop), we find that FDF reduces infections

and mortality in all epidemic scenarios, as long as supply constraints limit the vaccination rate to

1% of the population per day or less.4 We also find that using a less effective vaccine available

immediately instead of waiting for a more effective one reduces infections and mortality. If a

70% effective vaccine is available immediately while a 95% effective vaccine is available in two

months, starting vaccinations with the immediately available vaccine would reduce infections by

11–22% and deaths by 20–37%.

Trials to assess the impact of alternative doses on immune response for a variety of vaccines

and doses would involve a few hundred people each and could yield preliminary results within

weeks. One such trial is currently underway in Belgium (ClinicalTrials.gov ID NCT04852861).

Additional trials could be conducted in settings with little or no disease transmission, and among

low risk populations. Armed with information from such trials, or even with the data currently

available from early stage clinical trials, some jurisdictions might decide to try alternative dosing

at scale accompanied by rigorous data gathering, just as the UK and a few other countries decided

to implement FDF before complete data on first-dose efficacy was available. For example, a city in

Brazil has recently begun an experimental roll-out of half-doses of ChAdOx1 nCoV-19 (the vaccine

developed by Oxford and AstraZeneca, and manufactured by multiple organizations: AstraZeneca,

FIOCRUZ, R-Pharm, SK Bioscience, and Serum Institute of India (Covishield)) to non-elderly

adults (Governo ES, 2021). If alternative doses were found to have sufficiently high individual

efficacy based on observational data, these pilots could be scaled up. If not, those who received

4Hybrid stretching policies, using status quo dosing regimens for seniors at greatest mortality risk and stretcheddosing for younger people, can sometimes dominate the “pure” FDF approach, especially for averting deaths.

3

alternative doses could receive full doses, either of the original vaccine or of another vaccine (as

was done for some viral vector vaccines, or vaccines found to be less effective).5 Because tests of

alternative dosing are largely reversible and the potential benefits are so great, the costs of these

tests would be tiny relative to the expected benefits if there is even a modest chance such policies

could succeed. Additionally, alternative dosing can be implemented among some age groups only

(e.g. in non-elderly populations), which would further reduce any risks.

Accelerating vaccination with dose-stretching policies would not only reduce infections and

deaths, but also promote equity between groups or countries at opposite ends of the global queue

for vaccines. For example, if people at the end of the queue would currently wait two years to

be vaccinated, doubling supply would reduce their wait time by a full year. For someone near

the front of the queue expecting to be vaccinated in a single month, doubling supply would move

their vaccination forward by only two weeks. Additionally, rapidly vaccinating as many people as

possible could reduce the likelihood of more dangerous variants emerging globally.

Finally, it is worth noting that switching to smaller doses might not just yield an equivalent

vaccine, but could also potentially reduce side effects, yielding a superior vaccine.

Our paper adds to a recent literature studying optimal vaccine prioritization,6 which focuses

on the order in which different groups of people should be served by a fixed supply of vaccine

under different epidemic scenarios and efficacy assumptions. Our methods are similar, but our

question is different: we focus on ways that a fixed supply can be stretched to protect more people

5Effectiveness of mixing different vaccines has already been established in practice. For example, an ongoing trialin Spain found strong antibody response when combining ChAdOx1 nCoV-19 and BNT162b2 (ClinicalTrials.gov IDNCT04860739).

6See Akbarpour et al. 2021; Bubar et al. 2021; Gallagher et al. 2020; Hogan et al. 2020; Matrajt et al. 2020; Paltielet al. 2020. Our model only considers scenarios in which an older population cohort must finish vaccinations beforethe next cohort becomes eligible. In practice, however, logistical constraints often mean it is not possible to maintainstrict prioritization. In some cases it may also be more beneficial to vaccinate age groups in a different order. We willexamine this in future work.

4

while potentially sacrificing some individual efficacy. Under normal circumstances, when there

is no constraint on vaccine supply, public health is well served by designing vaccine regimens

to maximize individual health. In a pandemic, however, vaccination rates may be constrained

by vaccine supply, and there may be a race to vaccinate people before they get infected. In this

scenario, the vaccine regimen maximising individual protection might differ from the socially

optimal one. Individuals may benefit more from lower efficacy regimens if they allow for an

increase in vaccination rates and, consequently, a decrease in overall infection risk. This paper

uses simulations to provide quantitative results for impact of dose stretching in realistic epidemic

scenarios calibrated to the COVID-19 pandemic. In a companion paper (in progress), we provide

qualitative theoretical results on the optimality of dose stretching that hold generally for a more

abstract epidemiological model.

The rest of the paper is organized as follows: Section 2 discusses available data on the poten-

tial impact of dose stretching policies on efficacy; Section 3 and Section 4 respectively present

the epidemiological model and simulation methods; Section 5 estimates the public health im-

pact of speeding up vaccination; Section 6 analyzes a series of specific dose-stretching policies—

alternative dosing, longer delays between first and second dose, and utilizing available vaccines

rather than waiting for higher efficacy ones—under a variety of assumptions regarding efficacy.

We discuss next steps for testing dose stretching policies and the option value of undertaking such

testing in Section 7 and conclude in Section 8.

5

2. Evidence on Efficacy Under Dose-Stretching

In this section we consider evidence on the efficacy of various dose stretching policies, both from

clinical trials and from real world vaccination roll-outs.

Alternative dosing for COVID-19 has not yet been tested outside of early stage clinical trials.

However, we do have evidence from previous epidemics that very small doses can prove effective

in some cases. For example, Brazil successfully used 1/5-doses of yellow fever vaccine to combat

an epidemic in 2018 based on advice from the WHO (Pan-American Health Organization 2018).

Alternative dosing has also been considered for seasonal influenza (Antony et al., 2020; Pan-

American Health Organization, 2009).

Existing evidence from clinical trials suggests that alternative doses of some vaccines could

yield high immune responses, comparable to those for standard doses of the same vaccines, and

greater than those for some other, already approved vaccines. For example, a trial using ChAdOx1

nCoV-19 (Oxford/AstraZeneca) found that “differences in normalized titre levels [of neutralizing

antibody (nAb)] for the standard dose and a low dose [of approximately 1/2 of the standard dose]

within [18-55, 56-69, and 70+] age groups were not statistically significant” (Ramasamy et al.

2020). A trial with mRNA-1273 (Moderna) likewise found similar immune responses for both 50

and 100µg (standard) doses (Chu et al. 2021). This suggests significant scope for flexibility in vac-

cine dosage. This was acknowledged by the scientific advisor to the US’s Operation Warp Speed,

Moncef Slaoui, who in January 2021 suggested giving half doses of mRNA-1273 to some adults

(Wu, 2021). Recent comments from some vaccine manufacturers agree: Melissa Moore, Chief

Scientific Officer for Moderna, discussing vaccine boosters, said that the high dose of mRNA-

1273 was used to "guarantee effectiveness" but that she is confident doses would decrease in the

6

future, "reducing side effects without compromising protection" (Weintraub 2021).

Recent research also suggests that immune response, as measured by neutralizing antibody

(NAb) levels, is highly predictive of protection from symptomatic infection, both among conva-

lescent patients and among the vaccinated. Khoury et al. (2021) find a “remarkably predictive”

logistic relationship between NAb levels and vaccine efficacy (Spearman ρ of 0.905).7

In Figure 1 we use Khoury et al.’s model (fitted to standard doses of vaccines) and then, as-

suming the relationship between immune response and efficacy holds, plot additional points based

on immune response for different doses of currently used vaccines to add points for alternative

doses. Underlying data are given in Table 2 in Appendix A.8 Despite the exploratory nature of this

approach, the results strongly illustrate the potential benefits of adopting alternative doses. We ob-

serve that for some vaccines, immune responses associated with high efficacy can be obtained even

with much smaller doses. For mRNA-1273 (Moderna), for example, doses 1/2 and 1/4 of the stan-

dard both have immune response levels associated with 90-95% efficacy. For BNT162b2 (Pfizer)

there is no significant decrease in NAb level for a 2/3 dose in non-elderly populations (albeit with

a very small sample size), while NAb levels are associated with efficacy between roughly 70% and

85% for other dose-age combinations. For other vaccines, we also sometimes observe unexpected

trends, where lower doses lead to NAb levels associated with higher efficacy (e.g., NVX-CoV2373

(the vaccine developed by Novavax and not yet approved for distribution) and ChAdOx1 nCoV-

19 (Oxford/AstraZeneca)). While these results are not necessarily unrealistic (AstraZeneca, 2020),

they may be a consequence of limitations of the Khoury et al. modeling approach, or of uncertainty

7Data are based on phase 1-3 clinical trials for subsequently approved vaccines, which are publicly available. Asimilar relationship has also been reported by Earle et al. (2021).

8Where available, we used the same studies referenced by Khoury et al. to derive ratios of alternative dose tostandard dose immune response. The exceptions were: the 25µg dose of mRNA-1273 (Moderna), for which we usedChu et al. (2021); for BBV152 (the vaccine developed and manufactured by Bharat Biotech, sold as “Covaxin”), Ellaet al. (2021); for ChAdOx1 nCoV-19 (Oxford/AstraZeneca), Ramasamy et al. (2020).

7

Mean Neutralizing Antibody Level

Alternative Doses (Elderly)

Alternative Doses (Adults)

Standard Doses

mRNA-1273 (Moderna) 100µg

NVX-CoV2373 (Novavax) 5µg

BNT162b2 (Pfizer) 30µg

rAd26-S+rAd5-S (Sputnik) 1e11v.p.

CoronaVac (Sinovac) 3μg

BBV152 (Covaxin) 6µg

ChAdOx1 nCoV-19 (AstraZeneca) 5e10v.p.

JNJ-78436735 (Johnson & Johnson) 5e10v.p.

Standard Dose

0.1 1.0 10.0

100

90

80

70

60

50

40

Convalescent

mRNA-1273 25µg 25% of Standard DosemRNA-1273 50µg

Adults 18-55 (N=78) · Elderly 55+ (N=63)Adults 18-55 (N=15)

NVX-CoV2373 25µg 500% of Standard Dose

Adults 18-59 (N=50)

50% of Standard Dose

BBV152 3µg 50% of Standard Dose

Adults 12-65 (N=190)

ChAdOx1 nCoV-19 2.2e10v.p. 44% of Standard Dose

Adults 18-55 (N=41) · Elderly 56+ (N=62)

JNJ-78436735 1e11v.p. 200% of Standard Dose

Adults 18-55 (N=24) · Elderly 65+ (N=50)

BNT162b2 10µg 33% of Standard Dose

Adults 18-55 (N=12) · Elderly 65-85 (N=12)

BNT162b2 20µg 67% of Standard Dose

Adults 18-55 (N=12) · Elderly 65-85 (N=12)

Prot

ectiv

e E

�ca

cy (

%)

Figure 1: Efficacy Associated with Mean Neutralization Levels for Alternative Doses. The curve follows themodel derived by Khoury et al. linking NAb levels to protection from symptomatic infection for standard dosesof eight vaccines and in convalescents, with the shaded area corresponding to the 95% confidence interval of themodel. Lighter data points represent the mean (normalized) immune response and clinical efficacy of specific vaccines(referred to by colors) at standard doses, following Khoury et al.; response in convalescents is also plotted. NAb levelsfor vaccines are normalized to those of convalescents using clinical trial data for each vaccine. We calculate the ratiosof mean NAb responses for alternative versus standard doses using data from clinical trials that tested different doses.We then plot the alternative doses on Khoury et al.’s immunogenicity-efficacy curve as darker shapes. Doses for theelderly are represented by diamonds while doses for non-elderly adults (or all adults, where data is not available byage) are represented by circles. For consistency, if multiple age groups were compared, we use the immune responseto the standard dose in younger adults to normalise mean NAb levels. We note small sample sizes, typical of earlystage trials, and do not include measures of uncertainty.

inherent in early-stage clinical trials (including small sample sizes), or both.

As discussed by Khoury et al., a comparison across clinical trials of different vaccines may

be biased. Moreover, the relationship that holds across vaccines may not hold across doses of a

given vaccine. The entire curve traced by Khoury et al. may be shifted downward for some viral

variants. Recent studies have found a significant decrease in immune response from vaccines for

newer variants such as Delta.9 This could potentially change the relative benefits of using reduced

versus standard doses for some vaccines, but would most likely not change that reduced doses

of some vaccines may be more protective than full doses of others. More research is needed to

establish the absolute level at which there is protection from infection or severe outcomes, how

NAb levels affect efficacy against variants, and how decreases in NAb levels impact longevity of

protection (Hall et al. 2021, Krammer 2021).10 On the other hand, another analysis in the same

paper by Khoury et al. also suggests that even small NAb responses are protective against severe

disease and death, potentially increasing the value of alternative dosing. Regardless, our analysis

suggests that within-vaccine variations in efficacy are in many cases small compared to differences

across vaccines. We return to the discussion of these results in light of our simulation analysis in

Section 6.

In contrast to alternative doses, there is considerable evidence on the potential efficacy of a

delayed dosing interval between first and second doses—or “first dose first” (FDF)—as such poli-

9Wall et al. (2021) reports NAb levels after two doses of BNT162b2 that are 5.8 times higher for the original Wild-type virus first detected in Wuhan, China in December 2019 than for the Delta variant, detected in India one year later.Liu et al. (2021) estimates an immune response to the BNT162b2 vaccine that is 1.5 times higher for the Wild-typethan for the Delta type. Stowe et al. (2021) reports estimates of vaccine efficacy against symptomatic infection usingobservational data and conclude that efficacy against the Wild-type virus for the BNT162b2 vaccine was 93% whilefor the Delta type it was 88%. A similar study (Sheikh et al., 2021) reports a larger drop in efficacy, from 92% to 79%,again with the BNT162b2 vaccine.

10In addition, there are other determinants of vaccine effectiveness; for example, ChAdOx1 nCoV-19 has beenshown to elicit a much stronger T cell response than BNT162b2 among the elderly (Parry et al. 2021).

9

cies have already been enacted in several countries. For example, the default three- to four-week

delay for BNT162b2, ChAdOx1 nCoV-19, and mRNA-1273 has been stretched to 12 weeks in the

United Kingdom and 16 weeks in Canada.11 India also recently decided to delay second doses,

first to 6-8 weeks and now to 12-16 weeks (The Times of India 2021).

The UK decision was initially motivated only by clinical trial evidence, including immune

response data (see Appendix A for a non-comprehensive summary of clinical trial evidence on

first doses). Subsequent large-scale observational studies, including from vaccination campaigns

in the UK and Israel, estimate that a first dose of BNT162b2 is approximately 75% effective at

preventing infections (Appendix A presents details of the evidence discussed here). Related studies

which also include data for ChAdOx1 nCoV-19 (Oxford/AstraZeneca) find that first doses are 78–

94% effective at preventing hospitalizations. Additionally, a recent study suggests that the second

dose of ChAdOx1 nCoV-19 is more effective (82.4%) when it comes at 12 weeks, rather than at

four weeks (54.9%) as tested in the initial clinical trial (Voysey, et al. 2021).

However, first dose efficacy is much lower for other vaccine-variant combinations. First doses

of BNT162b2 and ChAdOx1 nCoV-19 have been significantly less effective against the variants

of concern originating in South Africa (B.1.351), the UK (B.1.1.7), and India (B.1.617.2) (Burn-

Murdoch et al. 2021). A study of CoronaVac (the vaccine developed by Sinovac and manufactured

by multiple organizations: Sinovac, Instituto Butanta, Bio Farma, and Pharmaniaga) in Chile re-

ported good efficacy against the standard variant after two doses, but very low efficacy after one

dose (Dyer 2021, Taylor 2021).12 We also note, however, that as the number of natural infections

11In a joint statement the four UK Chief Medical Officers wrote: “We agree with [the Joint Committee for Vaccina-tion and Immunisation] that at this stage of the pandemic prioritising the first doses of vaccine for as many people aspossible on the priority list will protect the greatest number of at risk people overall in the shortest possible time andwill have the greatest impact on reducing mortality, severe disease and hospitalisations and in protecting the NHS andequivalent health services” (UK Department of Health 2020).

12We provide references and summarize information from these trials in Appendix A. We note that efficacy of first

10

in a community increases, the risk of providing just a single dose decreases, since some evidence

suggests that a single shot provides as much protection for those who have been previously infected

as two doses in those never infected (Ebinger et al. 2021; Stamatatos et al. 2021; Willyard 2021).

Some countries have also decided to use vaccines that were available immediately rather than

waiting for more effective ones. For example, the UK, Europe, and Canada rolled out vaccina-

tions with a combination ChAdOx1 nCoV-19 and BNT162b2, rather than waiting for more mRNA

vaccines to be available. Chile and Seychelles have relied significantly on CoronaVac, with less ro-

bust efficacy data, to start vaccination campaigns earlier. Case rates remain high in both countries

(Mathieu et al. 2021), although the vaccine does appear to be protective against hospitalization and

death (as suggested in a recent study in Serrano, Brazil, where almost the entire adult population

has been vaccinated (e.g., Pearson 2021)).

The epidemiological modeling that follows excludes the potential impact of dosing stretching

polices on immune escape through mutation. Some have argued that dose stretching policies might

exacerbate this risk due to a prolonged period of partial immunity increasing the risk of immune

escape. However, many epidemiologists now believe that dose stretching may instead reduce the

probability of immune escape (e.g., Cobey et al. 2021). We expand on the current evidence in

Appendix A.

In summary, FDF approaches and using available vaccines early rather than waiting for more

effective ones have been tested as vaccination campaigns rolled out. We therefore have good

information on their effectiveness. We do not yet have efficacy data for alternative doses, but

immune response data suggests that smaller doses of some vaccines may be very effective.doses is also broadly consistent with the relationship between immune response and efficacy against symptomaticinfection as laid out by Khoury et al.. nAB levels from two doses are typically several times higher than for one dose,so while single doses may be sufficient for high efficacy against the original SARS-CoV2 virus, they may be lesseffective against variants with some degree of immune evasion.

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3. Epidemiological Model

Since the evidence on alternative dose efficacy is not dispositive, we model the potential impact

on the pandemic of a range of efficacy levels using a standard epidemiological model. The model

we use extends the canonical susceptible-exposed-infectious-recovered (SEIR) model, which is

widely used in mathematical epidemiology to characterize the spread of an infectious disease in a

closed population (Kermack and McKendrick 1991, Anderson and May 1992). The SEIR model

assumes individuals flow between disease and vaccination states over time, with sizes of population

in each state changing according to a set of differential equations. We extend the canonical SEIR

model to allow for death and vaccination (which is ineffective for some individuals), yielding the

following equations:

Si(t) =−λi(t)Si(t)− vi(t)δiSi(t) (1)

Ei(t) = λi(t)[Si(t)+Ni(t)]− γ′Ei(t) (2)

Ii(t) = γ′Ei(t)− γ

′′i Ii(t) (3)

Di(t) = piγ′′Ii(t) (4)

Ri(t) = (1− pi)γ′′Ii(t)− vi(t)δiRi(t) (5)

Pi(t) = vi(t)δi[eSi(t)+ Ri(t)

](6)

Ni(t) = vi(t)δi(1− e)Si(t)−λi(t)Ni(t). (7)

Dots denote derivatives with respect to time. Uppercase letters denote population compart-

ments (i.e., the fraction of the population in a given state): S for susceptible, E for exposed (in-

dividuals carrying the virus, but who are not yet contagious), I for infectious, R for recovered,

12

S E I

D

R

Vaccinated

P N

Figure 2: Compartment Flows in Epidemiological Model. Model described by Equations (1)–(7). Solid black linesreflect virus model and dashed lines vaccination. The full model has separate compartments for each age group i.

D for dead, P for protected by vaccine, and N for vaccinated but not protected. The population is

divided into G age cohorts, indexed by i = 1, . . . ,G, with respective sizes ni. Subscripting compart-

ments by i allows for different epidemic evolution across age cohorts. Tildes denote the size of the

compartment in proportion to both compartments receiving vaccines (susceptible and recovered)

i.e.,

Si(t) =Si(t)

Si(t)+Ri(t)(8)

Ri(t) =Ri(t)

Si(t)+Ri(t). (9)

Figure 2 depicts the population flows between the compartments described in equations (1)–(7).

Our initial model assumes a single vaccine, either with a single dose, or where efficacy does not

change between two doses. Lowercase letters denote model parameters governing the evolution of

compartments. All parameters except e are age-specific, as denoted by subscript i. γ ′ and γ ′′ are,

13

respectively, the hazard rates of moving from exposed to infected and from infected to recovered

or dead. These are estimated as the reciprocals of the durations of the virus’s incubation period and

of the infectious period, respectively. The rate of new infections equals λi(t), described in further

detail below. Parameter pi is the mortality risk. Vaccine efficacy, denoted e, is the probability the

vaccine protects from infection. The model makes no distinction between the vaccine’s efficacy

(performance measured in clinical trials) and effectiveness (performance in practice in the popula-

tion); e is used to denote both interchangeably. We assume recovered individuals (compartment R)

are perfectly protected by vaccination and that exposed or infectious individuals (compartments E

and I) are not vaccinated.

To account for vaccine prioritization, we introduce an indicator variable vi(t), switching from

0 to 1 on the day age cohort i becomes eligible for vaccination and to 0 again at the point where all

willing members of the cohort have been vaccinated. Reflecting common practice, we assume older

cohorts must finish vaccinations before the next cohort becomes eligible.13 When vi(t) = 1, age

cohort i is vaccinated at a constant rate δi, drawing on a continuous stream of vaccine production

from a given capacity. To keep track of cumulative doses distributed, we introduce the auxiliary

compartment V , where Vi(t) = δivi(t), and where V (t) is the proportion vaccinated in the entire

population.

The rate of new infections, λi(t), depends on the number of daily contacts a susceptible in-

dividual has with currently infectious individuals. To reflect differences in interaction across age

cohorts, we use a contact matrix C, where entry c(i, j) ≥ 0 denotes the number of contacts made

13Most recent studies, e.g. by Bubar et al. (2021), find that vaccination of those aged 60 and older reduces thehealth burden more than for other age groups under a wide range of scenarios, especially in high-income countries.On the other hand, Matrajt et al. (2020) find that vaccinating high-transmission groups (including children) first can beoptimal if the vaccine is highly effective and supply is very large, conditions that often apply to infectious diseases suchas seasonal influenza outside of a pandemic. We will investigate different prioritization strategies in future versions ofthis work.

14

by an individual in cohort i with an individual in cohort j. To derive the proportion of each age

group infected at time t, each contact is scaled by the probability of virus transmission on contact,

q, and probability that the contacted person is infected, I j(t), yielding

λi(t) = qG

∑j=1

c(i, j)I j(t). (10)

For a given C, q can be adjusted to match any desired reproductive number R for the virus (i.e., the

number of secondary cases produced by a single infection).

The initial conditions of the system (1)–(7) require specifying the proportion of the population

that is susceptible S(0), immune R(0), and infectious I(0) at the outset of the epidemic. We take

I(0) to be small and for simplicity take E(0) = I(0). We assume that the proportion of each age

cohort in each initial compartment is the same as in the overall population.

4. Simulation Methods and Parameters

This section discusses some of the main assumptions of the model and parametrization. A complete

list of the parameters used in the simulations is provided in Table 3 in Appendix D. Here we

highlight the most critical parametric assumptions. We discuss initial conditions in Section 4.1, the

time horizon covered by the simulation in Section 4.2, assumptions related to disease spreading

and burden in Section 4.3, assumptions concerning vaccination efficacy and constraints in Section

4.4, and the simulation methods in Section 4.5.

15

4.1. Initial Conditions

We run simulations for three illustrative epidemic scenarios. The slow decrease scenario sets the

initial effective reproduction rate to R= 0.99 and initial infectious proportion to I(0) = 1%.14 This

scenario may capture a situation in which non-pharmaceutical interventions (NPIs) are introduced

following an epidemic wave but are only effective enough to decrease cases slowly. The slow

growth scenario sets R = 1.1 and I(0) = 0.5%, perhaps reflecting a situation in which NPIs are

not effective enough to prevent a subsequent wave of infections, such as the one experienced by

the United States in late 2020. The fast growth scenario sets R = 2 and I(0) = 0.1%, e.g., a case

when a new virus strain suddenly emerges, thwarting previously effective NPIs (such the one as

observed in the United Kingdom in December 2020, or the emergence of the P.1 variant in Brazil

in late 202015). In both growth scenarios, I(0) is adjusted so that the peak of infections occurs

three to four months from the start of vaccinations.16

We choose parameters for initial immunity that broadly reflect the state of the COVID-19

pandemic in early 2021. We assume 20% of people aged 20 and over have immunity acquired

from infection, leaving 80% susceptible. To reflect the lower clinical case rate in the younger

population (Davies et al. 2020; Goldstein, Lipsitch, and Cevik 2020), we assume only 50% of

under 20s are susceptible.14Since we will assume 20% of pre-existing protection in people aged 20 and over, the initial effective reproductive

number R is lower than R0, the basic reproductive number in a fully susceptible population.15See Sabino et al. 2021.16Assuming that the epidemic peaks earlier or that vaccinations start in the declining phase of the epidemic would

decrease measured vaccine benefits, as discussed in Section 6.1.

16

4.2. Time Horizon

Each simulation runs for T = 365 days. This is sufficient time for the epidemic to die out in

the scenarios considered but, we assume, not long enough for unmodeled factors to come into

play, such as the alleviation of supply constraints with expanded capacity or the waning of vaccine

protection from initial doses, perhaps warranting booster shots.17 Similarly, we assume that there is

no natural loss of immunity (no flow from recovered to susceptible) during the simulation period.18

4.3. Infections and Deaths

We use a social contact matrix c(i, j) based on a large cross-country study of contacts between dif-

ferent age groups, primarily in European countries (Mossong et al. 2008). Our matrix is therefore

more representative of high-income countries, but we are not aware of comparable data on social

mixing in low-income countries. For most of the paper, cohort size (ni) and mortality risk (pi)

for different age cohorts is based on data for high-income countries, although we also perform a

separate analysis for low-income countries (see Appendix C). Throughout the age distribution, the

risk of death from COVID-19 increases rapidly with age, about three-fold per decade (Manheim et

al. 2021).

The model assumes that contact frequencies are independent of infection risk, precluding be-

havioral changes in response to changes in infection risk as the epidemic progresses. The model

assumes that contact frequencies are independent of infection risk, precluding behavioral changes

in response to changes in infection risk as the epidemic progresses. Since we abstract from the

17The choice of T might play a bigger role in models where the reproductive number is close to 1, for example, dueto behavioral responses to risk, as in Gans (2020).

18Muena et al. (2021) show that neutralizing antibody responses can persist up to 12 months after infection. Hall etal. (2021) show high levels of protection at six months after infection. In both cases, the upper limit is due to the lackof longer-term data at the time of publication.

17

emergence of viral variants, epidemics always have a single peak and fade out when the virus’s

effective reproductive number satisfies R≤ 1, which happens when a sufficiently high fraction of

population is protected, either by vaccination or recovery from natural infection.

4.4. Vaccination

The base case for vaccination is a 95% effective vaccine, when used as tested in Phase 3 trials

(standard dosing, with a delay between two doses). We assume that those under 20 (constituting

22% of population in our base case simulations) receive no vaccination. To account for vaccine

hesitancy, we assume 20% in each age group refuse vaccination. We assume that the vaccine

becomes effective 10 days after it is administered.19

As of early May 2021, the world is vaccinating at a rate of approximately 0.25% of the pop-

ulation per day (Mathieu et al. 2021), our base case immunization speed.20 At the high end, the

United Kingdom, United States, Canada, Chile and Israel have all managed to vaccinate at rates

well above 0.8% of the population per day;21 however, the current median global rate of vacci-

nation (as of May) is only 0.27% of the population per day (Mathieu et al., 2021). Thus, at a

global level, supply rather than delivery logistics or demand (e.g., vaccine hesitancy) seem likely

to constrain full vaccination well into 2022, and perhaps for considerably longer.

Accordingly, our model is intended to apply to contexts in which vaccination rates are con-

strained primarily by the available supply.22 While this may not apply for some countries, this

19We achieve this by treating vaccinated compartments in the model as “effectively vaccinated”. Hence if vaccina-tions in a given age group start of day t1 and end of t2, we start the flow into vaccinated compartments on date t1 +10and stop it on t2 +10.

20The world rate of vaccination has been increasing since early May, driven in part by China.21Over two weeks in April and May, Mongolia was vaccinating 2% of its population per day.22In general, we are also agnostic as to whether shortages are due to shortages in drug substance or, for example,

fill and finish capacity. With alternative dosing, the number of doses in each vial increases, so it alleviates constraintswherever they are in the production system. FDF and using lower efficacy vaccines early are more about the timing

18

seems broadly to be the case globally. The model could be extended to consider other scenarios

where, for example, delivery constraints might at some point be binding.

Additionally, while we treat efficacy as a scalar, in reality it is multidimensional: vaccines may

differ in efficacy against different variants, in duration of protection, or in their protection against

infection and disease.

4.5. Simulation Method

We generate a simulation run for each configuration of parameters by finding the deterministic

solution of the differential-equation system consisting of these equations (1)–(7) using standard

numerical methods.23

Figure 3 illustrates the evolution of vaccinations and infections for the various epidemic sce-

narios and vaccination rates analyzed. We will discuss the impact of vaccination below. With no

vaccination, we find that from 8% (slow decrease scenario) to 55% (fast growth scenario) of the

population get infected during the simulation period. Individuals aged 20 to 49 are responsible

for between 55% and 59% (depending on the scenario) of all infections, assuming no vaccine.

This is consistent with recent findings by Monod et al. (2021), who estimated that three quar-

ters of infections in the US originated from individuals in that age bracket (albeit in a period with

school closures). Figure 13 in Appendix D illustrates the age-specific dynamics of vaccination and

infection in the model.

of vaccine use, and hence are orthogonal to where the constraints in vaccine supply are. If the constraints are in filland finish capacity only, then another option - filling more doses in each vial - also becomes an option to alleviateconstraints. However, this is also likely to increase waste to some extent, and force more centralized, camp-stylevaccination approaches rather than vaccine delivery where people usually get health care, and so may eventually, insome contexts, make it hard to drive high take-up. This may also be true of alternative dosing - which effectivelyincreases the number of doses per vial.

23We solve all differential-equation systems using the odin package, version 1.0.8, and generate exhibits using R,version 4.0.2. All code used in this project is available at https://github.com/wwiecek/covstretch.

19

Vaccinated per day None 0.25% 0.50% 1.00%

0

20

40

60

0 120 240 360

Time (days)Cum

ulat

ive

vacc

inat

ions

(%

pop

.)

Vaccinations

Slow−decrease epidemic Slow−growth epidemic Fast−growth epidemic

0 120 240 360 0 120 240 360 0 120 240 360

0

1

2

3

4

5

0.0

0.1

0.2

0.3

0.0

0.1

0.2

0.3

Time (days)Cur

rent

infe

ctio

ns (

% p

op.)

Infections

Figure 3: Evolution of Vaccinations and Infections under Baseline Epidemic Scenarios. Colors indicate differentvaccination rates δ with a 95% effective vaccine. While the population is vaccinated at a constant rate, age priori-tization leads different age cohorts to start being vaccinated at different times. Cohorts aged 20 and above achieve80% vaccination coverage by time T = 365 days. Please note that the scales of the vertical axes vary according to theepidemic scenario. Figure 13 in Appendix D provides a finer breakdown of vaccination and infection dynamics by agecohort.

The outcome variables for our simulations are the burden of infection, defined as the proportion

of the total population that develop new infections during the simulation period, and the burden of

death, defined as the proportion of the total population that die during the simulation period. We

focus on these rather than alternative outcomes to present a reasonable number of results.24

5. Benefits of Speeding Vaccination, Holding Efficacy Constant

In this section we examine the potential impact of accelerating vaccination through a dose stretch-

ing policy if it entails no loss of efficacy. Section 5.1 considers increasing the rate of vaccination,

while Section 5.2 considers starting the vaccination campaign earlier. Subsequent sections consider

the case when dose stretching policies come at the cost of reduced efficacy.24Additional outcome variables could include hospitalizations and severe infections, both of which are correlated

with age. Our focus on counts of infections and deaths allows us to abstract from the delay between infection andillness or death, which would have to be parametrized in an analysis of healthcare use.

20

5.1. Faster Vaccination Rate

Increasing vaccination rates without sacrificing efficacy would dramatically reduce disease bur-

dens, as shown in Figure 4. For example, the bottom left panel indicates that vaccinating 0.25% of

the population daily averts 18–50% of infections and 46–71% of deaths across epidemic scenar-

ios. In contrast, if the vaccination rate was doubled to 0.5%, 41–70% of infections and 58–80%

of deaths could be averted. The top panels show that increasing vaccination rates reduces disease

burdens considerably more in absolute terms in the fast-growth scenario than in other epidemic

scenarios. This is not surprising since disease burdens are highest in this scenario.

Typically, faster vaccination reduces burden at a decreasing rate. This pattern is depicted by

the concavity of most of the burden reduction curves, especially for deaths. This effect is a conse-

quence of age prioritization: vaccinating the highest mortality risk people first allows more deaths

to be averted with relatively fewer vaccines. Higher vaccination rates mainly speed the vaccination

of lower mortality risk people. The biggest departure from decreasing returns to faster vaccination

is observed with infections in the fast-growth scenario, where some convexity can be seen in the

bottom panel. The pattern of the results across infections and deaths is roughly similar to that

found in other recent models of COVID-19 vaccination (Bubar et al. 2021; Hogan et al. 2020;

Matrajt et al. 2020).

5.2. Earlier Vaccination Start

Another way of speeding vaccinations is to start the vaccination campaign earlier. Figure 5 presents

results from simulations in which the start of the campaign is varied from four months before the

peak of the epidemic to three months after. We restrict attention to a fast-growth epidemic.

21

Epidemic scenario Slow−decrease Slow−growth Fast−growth

Infections Deaths

2.00

1.00

0.75

0.50

0.25

0.10

2.00

1.00

0.75

0.50

0.25

0.10

0.01

0.03

0.10

0.30

3

10

30

Percentage of pop. vaccinated daily

Bur

den

(% p

op.)

Burden (log scale)

Infections Deaths

2.00

1.00

0.75

0.50

0.25

0.10

2.00

1.00

0.75

0.50

0.25

0.10

0

25

50

75

100

0

25

50

75

100

Percentage of pop. vaccinated daily

% b

urde

n av

erte

d

Reductions

Figure 4: Benefits of Faster Vaccination. The top panels show simulation results for burdens under various vaccina-tion rates. The bottom panels show simulation results for the percentage reduction in burdens relative to no vaccination.In the left panels, we refer to the burden from infection, while in the right panels we refer to the burden from death. Inall scenarios we assume a 95% effective vaccine and sequential age prioritization.

Consistent with the results in the previous section, for any start date, the higher the vaccination

rate, the greater the burden averted. Additionally, for any vaccination rate, the earlier the campaign

is started, the greater the burden averted. Faster and earlier vaccination campaigns allow more

people to be protected before they are exposed to infection.

If the campaign starts early enough in the epidemic, the disease burden can be almost entirely

averted, even for low daily vaccination rates. Such behaviour is typical in deterministic com-

22

Vaccinated per day 0.10% 0.25% 0.50% 1.00% 2.00%

0

25

50

75

100

−4 −3 −2 −1 0 1 2 3

% in

fect

ions

ave

rted

Infections

0

25

50

75

100

−4 −3 −2 −1 0 1 2 3%

dea

ths

aver

ted

Deaths

Vaccination start (months after infection peak)

Figure 5: Burden Averted Varying Start of Vaccine Campaign. Simulation results for burden averted relative to novaccine with vaccination campaign having start dates before or after infection peak (horizontal axis). Different curvescorrespond to different vaccination speeds. Maintains baseline assumptions including 95% effective vaccine.

partmental models such as SEIR. At the other extreme, if the campaign does not start until the

population is close to herd immunity, the campaign hardly reduces disease burden, regardless of

the vaccination rate, since most infections and deaths will have already occurred.

6. Impact of dose stretching policies with efficacy trade-offs

This section provides simulation results on the health impact of a series of alternative dosing poli-

cies relative to the status quo, under a range of plausible assumptions regarding potential trade-offs

between these policies and individual vaccine efficacy. We analyze alternative dosing in Section

6.1, FDF in Section 6.2, and using an inferior vaccine that is available sooner in Section 6.3.

23

6.1. Alternative Dosing

Alternative dosing involves giving less than the standard dose of a vaccine to obtain more doses

from limited capacity.

Because we consider the case in which the pace of immunization is subject only to a supply

constraint, the vaccination rate is proportional to the reciprocal of dose size. So, for example,

using half rather than full doses would double the vaccination rate. In this section, we analyze the

impact of alternative dosing on the burden of infections and deaths while varying three variables:

dose fractions, efficacy reductions associated with moving to alternative dosing, and epidemic

scenarios.

We return to the baseline assumption that the vaccine is available from t = 0 and maintain the

other baseline assumptions, including that a full dose has 95% efficacy and can be supplied at a

rate of 0.25% of the population per day. We now assume that a dose fraction φ ∈ (0,1] can be used,

increasing the vaccination rate to 0.25%/φ . We initially consider dose size to be uniform across

age groups, but we discuss potential alternatives at the end of this section.

Figure 6 presents the simulation results, comparing the impact of alternative versus full dosing.

Using the estimated efficacies suggested by our exploration in Figure 1, we can estimate the

potential benefits of alternative dosing. For illustration, we consider the cases of three of the

vaccines with largest production: mRNA-1273 (Moderna), BNT162b2 (Pfizer), and ChAdOx1

nCoV-19 (Oxford/AstraZeneca). For mRNA-1273, a half dose leads to NAb levels associated with

an efficacy of approximately 95%. In this case, moving to half doses would avert 24–29% of

infections and 22–47% of deaths. For BNT162b2, a 1/3 dose produces NAb levels associated with

approximately 80% efficacy, so moving to 1/3 doses would reduce 34–52% of infections and 25–

24

49% of deaths. Although not shown in our results (efficacy of a standard dose is not 95%), halving

the dose of ChAdOx1 nCoV-19 would also lead to reductions in infections and deaths, as there is

no observed impact on immune response and therefore no associated loss of vaccine efficacy in

comparison to the standard dose.

Significant gains are possible even if the expected efficacies of alternative doses are not as high

as those presented above. For the epidemic scenarios that we consider, moving from a full to a half

dose (thereby doubling vaccination speed to 0.5% per day) reduces the burden of infections and

death as long as efficacy is at least 70%. Moving from a full to a quarter dose (thereby increasing

speed four-fold, to 1% per day) decreases the burden of infections and death even if efficacy drops

to 50%. The health benefits can be substantial: for example, moving from a full to a half dose that

is 80% as effective reduces the burden of infection by 21–36% relative to that of using the full dose

regimen, depending on the epidemic scenario, while reducing deaths by 14–25%.

We find that alternative doses generally reduce infections more than deaths. For example,

moving from a full to a half dose that is 50% as effective reduces infections across all epidemic

scenarios, but increases deaths. The reason is that the baseline vaccination rate of 0.25% per day is

already fast enough to protect older cohorts with high mortality risks, given they receive priority in

vaccination. Therefore, further speed gains do not offset the decrease in efficacy for older groups.

The potential for increasing the burden of deaths by reducing efficacy is particularly apparent in

the fast-growth scenario, where a half dose increases death burden unless its efficacy is at least

70%. Hence, trade-offs between efficacy and speed are sensitive to both epidemic context and the

burden measure prioritized by the policymaker.

Our base case assumed a daily vaccination speed of 0.25% per day. We replicate our analysis

for vaccination speeds between 0.1% and 2%, with results presented in Figure 14 in Appendix D.

25

0.54

0.49

0.46

0.44

0.42

0.41

0.68

0.64

0.61

0.58

0.56

0.55

0.76

0.72

0.69

0.66

0.64

0.63

0.88

0.85

0.82

0.79

0.77

0.76

1.01

0.98

0.96

0.93

0.91

0.90

1.10

1.07

1.05

1.03

1.01

1.00

0.74

0.68

0.63

0.58

0.55

0.53

0.86

0.79

0.74

0.69

0.65

0.63

0.93

0.86

0.80

0.75

0.70

0.68

1.05

0.98

0.91

0.86

0.80

0.78

1.18

1.11

1.04

0.98

0.93

0.90

1.28

1.21

1.14

1.08

1.03

1.00

0.36

0.32

0.29

0.26

0.25

0.24

0.51

0.46

0.42

0.39

0.37

0.36

0.60

0.55

0.51

0.48

0.45

0.44

0.78

0.72

0.68

0.64

0.61

0.60

1.03

0.96

0.91

0.87

0.83

0.81

1.22

1.16

1.10

1.06

1.02

1.00

0.60

0.52

0.46

0.41

0.38

0.36

0.76

0.66

0.59

0.53

0.48

0.46

0.87

0.76

0.67

0.60

0.54

0.52

1.08

0.94

0.84

0.75

0.68

0.64

1.36

1.21

1.08

0.97

0.87

0.83

1.61

1.44

1.29

1.16

1.05

1.00

0.50

0.37

0.27

0.19

0.14

0.13

0.60

0.50

0.42

0.35

0.29

0.27

0.73

0.65

0.57

0.51

0.46

0.43

0.92

0.87

0.82

0.77

0.73

0.71

1.04

1.01

0.98

0.95

0.92

0.91

1.09

1.07

1.05

1.03

1.01

1.00

0.81

0.54

0.33

0.20

0.12

0.09

0.96

0.71

0.51

0.36

0.24

0.20

1.12

0.88

0.68

0.51

0.37

0.31

1.38

1.16

0.96

0.77

0.61

0.53

1.60

1.40

1.21

1.04

0.87

0.79

1.75

1.57

1.40

1.24

1.08

1.00

Slow−decrease epidemic Slow−growth epidemic Fast−growth epidemicInfections

Deaths

13/

41/

21/

31/

41/

8 13/

41/

21/

31/

41/

8 13/

41/

21/

31/

41/

8

0.5

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0.7

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0.9

0.95

Dose fraction

Effi

cacy

of f

ract

iona

l dos

e

Fractional dose better by >5% Comparable (within 5%) Full dose better by >5%

Figure 6: Burden Averted under Full Relative to alternative dosing. Entries present simulation results for the ratioof burden averted under full relative to alternative dosing; greater than 1 (emphasized by darker background) favors fulldosing and less than 1 (emphasized by lighter background) favors alternative dosing. Each tile represents a differentcombination of epidemic growth, level of efficacy of alternative dose, and size of alternative dose, proportional toreciprocal of vaccination rate. The same baseline assumptions hold, including that the full dose is 95% effective andthe vaccination rate is 0.25% of population per day. These results also apply to the comparison of a less effectivevaccine with greater supply against a smaller supply of a more effective one.

Predictably, we find that adjusting dose size is sensitive to all factors that we investigate (epidemic,

vaccine supply, loss of efficacy from alternative dosing). However, alternative dosing is preferred

in most situations, with the exception of fast-growing epidemics combined with a large vaccine

supply.25

The alternative dosing policies we have discussed here are uniform across age cohorts. In sim-

ulations, we found that switching from uniform to age-varying doses produces only small gains

relative to switching from full doses to the optimal uniform alternative dose.26 However, as evi-

25For example, if a half dose is 80% effective, then it would reduce deaths and infections relative to a 95% effectivedose under all scenarios, except if the epidemic is growing fast (R= 2) and daily vaccinations with full dose are at 1%of the population or more.

26For example, in a fast-growing epidemic, vaccinating 30% of the population (with age prioritization) averts 82%

26

denced by clinical trial data, it is likely that for some vaccines, efficacy will vary across age groups.

In such situations, the additional benefits from using age-varying an alternative dosing strategy will

be larger.

The three vaccines discussed above (mRNA-1273, BNT162b2, ChAdOx1 nCoV-19) are among

those with the largest production levels, with total manufacturing of approximately 5-6 billion

doses projected for 2021 (Burger 2021, Moderna 2021, AstraZeneca 2021). The majority of these

doses have not yet been delivered to people’s arms, and so could potentially be available for al-

ternative dosing. Moderna has also announced plans to increase production to 3 billion doses in

2022. Although it is hard to accurately predict the number of extra doses that would be generated

from alternative dosing, these figures give us an idea of the huge potential for extra supply that

could come at no or little cost to efficacy. These benefits could also be available quickly, unlike the

benefits of expanding production, which occur with some delay.

6.2. First Doses First

Next, we consider the effect of delaying the second dose of a two-dose vaccination course so that

more people can receive their first dose sooner. Here too we vary assumed efficacy of the first dose

to understand under what range of efficacies the alternative policies are preferred.

The basic model in equations (1)–(7) needs to be extended to allow one or two doses to have

differing efficacy and to connect the delay between doses to the rate of vaccination. We maintain

the assumption that a single vaccine candidate is available. Figure 7 provides a schematic diagram

of the compartment flows in the extended two-dose model. Differential equations are provided in

of deaths suffered under no vaccination. The optimal uniform alternative dose is 3/10 of a full dose, averting 93.3%of deaths under no vaccination. The optimal age-varying alternative dosing scheme averts 93.6% of deaths under novaccination, only 0.3% more.

27

N1

S E I

D

R

Dose 1

Dose 2

P1

N2P2

Figure 7: Compartment Flows in Model with Two Doses. Model described by equations (B1)–(B9) in Appendix B.Additional notes from Figure 2 apply.

Appendix B.

Subscripts 1 and 2 indicate variables associated with the first and second doses. Thus, compart-

ments P1 and N1 contain people protected or not, respectively, following their first vaccine dose.

First doses are administered at a rate of δ1i in age group i, and efficacy for those vaccinated with

a single dose is e1. Individuals in compartments P1 and N1 receive a second vaccine dose at a rate

of δ2i. With probability e2, the second dose is effective and the recipient flows into compartment

P2; otherwise, the second dose is ineffective and the individual flows into N2. Let the auxiliary

variable Vi(t) = P1i(t)+N1i(t)+P2i(t)+N2i(t) denote cumulative vaccinations, counting both first

and second doses (so a cohort is double counted if all members receive both doses).

We take the status quo policy, second doses first (SDF), as requiring a four-week gap between

doses.27 Setting aside the ten days required to develop immunity, the effective gap is δ2i = 18

27For BNT162b2 (Pfizer) and mRNA-1273 (Moderna), gaps of three and four weeks, respectively, are recom-mended. Using the longer of the two gaps for the SDF baseline makes SDF look more like FDF and thus leads to amore conservative measure of the difference between the policies.

28

days for all age cohorts under a SDF policy.28 For the first doses first (FDF) policy, we assume

a delay of 12 weeks until second dose (δ2i = 74). We also consider a class of hybrid policies

(HDF-a), with a 12-week delay for those under age a and a 4-week delay for those a and over.

Hybrid policies maintain high levels of protection for older cohorts while prioritizing speed over

efficacy in younger cohorts. All simulations fix e2 = 0.95 but vary e1. As in previous sections, we

consider a range of vaccination speeds. Here, however, delicate calculations are required to ensure

the consistency of speed across alternative policies.29

Figure 8 shows the evolution of vaccine protection provided by one and two doses under SDF,

FDF, and HDF-60 policies for baseline parameters. FDF quickly provides protection to a greater

share of the population with the first dose than SDF; HDF-60 does not diverge from SDF until

all individuals aged 60 and over receive their first dose. The third panel verifies that the overall

speed of vaccinations is consistent across policies, as the paths of cumulative doses used virtually

overlap.

Figure 9 presents results on the ratio of benefits under the status quo SDF policy to benefits

under the best alternative policy, whether FDF or HDF-a. Benefits in the top panels are averted

infections and in the bottom panels are averted deaths. Each tile represents a different combination

28Same as in the earlier model, to account for this delay we set indicators vi(t) to correspond to effective vaccinationtimes, not time of injection.

29Fixing the target speed under examination, we first compute the δ1 needed to generate that speed under SDF as abaseline. We then compute the δ1 under FDF so that the time series of doses used matches that under SDF as closelyas possible. Since an exact match is impossible, we use the value of δ1 for FDF that minimizes the mean squared error.

T ′

∑t=1

[V FDF(t)−V SDF(t)]2

between the cumulative number of vaccine doses administered under FDF in each period, V FDF(t), and under SDF,V SDF(t), over the entire time period (T ′ = T = 365) or while vaccinations are happening (in case all those eligible andwilling to get vaccinated do so in less than one year). We compute V FDF(t) via simulation for a grid of integer values of1/δ1 and select the value minimizing the expression above. A similar procedure is used for HDF-a, with the exceptionthat the status quo vaccination rate is maintained for those aged a and over. For example, setting δ1 = 1/180 underSDF, the mean-squared-error minimization leads to δ1 = 1/145 under FDF. Under HDF-60, we maintain δ1 = 1/180for cohorts age 60 and over. The mean-squared-error minimization leads to δ1 = 1/155 for cohorts under age 60.

29

Had one dose, protected Had two doses, protected Cumulative doses

0 120 240 360 0 120 240 360 0 120 240 360

0

50

100

0

20

40

60

0

5

10

15

20

Time (days)

Pop

ulat

ion

%Second−dose delay policy: SDF HDF−60 FDF

Figure 8: Vaccine Coverage under Various Delays in Second Dose. Proportion of population protected by one dose(first panel) or two doses (second panel) under various policies, assuming e1 = 0.8 and e2 = 0.95. Note that the firsttwo panels do not show the total number of people that received one or two doses but rather the number of people thatreceived one or two doses and became protected. SDF refers to second doses first, the status quo policy of delayingfour weeks until the second dose; FDF refers to first doses first, delaying 12 weeks until the second dose; HDF-60refers to a hybrid policy of delaying four weeks for age 60 and over and 12 weeks for under 60. For SDF, we set1/δ1 = 0.25% vaccinated each day with the first dose and δ2 = 1/18. Then δ1 is adjusted for FDF and HDF-60 sothat the time series of total vaccinations across policies match (third panel). Note cumulative doses can exceed 100%as all individuals eventually receive two doses.

of epidemic growth, level of efficacy of first vaccine dose, and speed of vaccination campaign.

For most entries, a policy involving some stretching, either “pure” FDF or a hybrid (HDF)

policy, averts more infections and deaths than SDF. SDF does better only when the vaccination

rate is extremely high (2% of population per day receiving first doses under SDF) and the efficacy

of a single dose low (e1≤ 0.7 for the fast growth scenario and e1≤ 0.5 for slow growth). SDF does

better under those limited circumstances because such a rapid vaccination rate reduces scarcity and

the need to trade off efficacy versus speed.

FDF for all age groups is nearly always better at reducing infections than other policies. One

or another HDF policy is better at reducing mortality than FDF at the lowest levels of e1. FDF

increases protection for younger individuals, achieving reductions in community transmission, but

at the cost of reducing efficacy in the elderly, who face the greatest mortality risk.

30

0.99

0.96

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1.00

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1.00

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0.90

1.00

1.00

0.98

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0.93

1.00

1.00

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0.98

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0.96

1.00

0.96

0.93

0.90

0.88

0.87

0.90

0.86

0.84

0.82

0.80

0.79

0.88

0.85

0.82

0.80

0.79

0.78

0.88

0.85

0.83

0.81

0.80

0.79

0.94

0.92

0.91

0.89

0.88

0.87

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0.99

0.98

0.97

0.96

0.96

1.00

1.00

1.00

0.97

0.95

0.93

1.00

0.99

0.95

0.92

0.89

0.87

0.99

0.98

0.94

0.90

0.87

0.85

0.99

0.97

0.93

0.89

0.86

0.84

1.00

0.99

0.97

0.93

0.89

0.87

1.00

1.00

0.99

0.97

0.94

0.93

1.07

1.05

1.01

0.91

0.84

0.81

0.88

0.79

0.71

0.65

0.60

0.58

0.80

0.73

0.66

0.61

0.56

0.54

0.86

0.82

0.78

0.74

0.70

0.68

0.99

0.98

0.97

0.96

0.95

0.94

1.00

1.00

1.00

0.99

0.99

0.99

1.04

1.03

1.02

1.00

0.85

0.78

1.00

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0.76

0.62

0.56

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0.85

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1.00

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1.00

1.00

1.00

0.98

0.95

0.94

Slow−decrease epidemic Slow−growth epidemic Fast−growth epidemicInfections

Deaths

0.10

0.25

0.50

0.75

1.00

2.00

0.10

0.25

0.50

0.75

1.00

2.00

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0.95

Percentage of pop. vaccinated daily

Effi

cacy

follo

win

g fir

st d

ose

(e1)

policyFDF for all

FDF under 80

FDF under 70

FDF under 60

FDF under 50

SDF

Figure 9: Burden Averted under SDF Relative to Best Alternative Policy. Entries present simulation results forratio of burden averted under status quo SDF policy to best alternative. Greater than 1 favors SDF, and less than 1favors an alternative. Color indicates optimal policy, ranging from dark green when FDF is optimal to light purplewhen SDF is optimal, with an HDF policy optimal for colors in between. Each tile represents a different combinationof epidemic growth, level of efficacy of first vaccine dose, and speed of vaccination campaign. For a comparison of theburden averted under various vaccine policies relative to no vaccination rather than relative to each other, see Figure 16in Appendix D.

The relative benefit of delaying first doses varies with the vaccination rate in an inverted U-

shape. When the vaccine is rolled out very slowly, say, 0.1% first doses per day under SDF, FDF

averts no more than a few percentage points of disease burden, even if delay results in little to

no loss of efficacy. For intermediate vaccinate rates, FDF can avert substantially more burden

than SDF. For example, averted infections are 46% higher and averted deaths 48% higher for a

vaccination rate of 0.75% first doses per day under SDF under the fast-growth scenario. At very

high vaccination rates, the advantage of FDF shrinks or disappears as the supply constraint that

FDF was meant to relax effectively disappears.

In practice, FDF may be better than SDF or hybrid policies in reducing the burden of infection

31

and death in the population, provided the efficacy from the first dose is sufficiently high for some

COVID-19 vaccines. For vaccines for which efficacy following first dose drops below 80%, a

hybrid policy may be best. Conclusions about the relative benefits of FDF policies are sensitive to

assumptions about efficacy, epidemic growth, and vaccination rate.

6.3. Using Available Vaccines Immediately Versus Waiting for More Effective

Vaccines

Some countries may face a choice between using a vaccine available immediately or waiting in a

queue for a more effective vaccine.

If the planner has to choose one vaccine or the other and cannot switch later when the more

effective vaccine becomes available, analysis of the optimal country decision is straightforward

using simulations based on the basic model. The trade-offs are similar to those involved in alterna-

tive dosing: speeding supply at the cost of lower efficacy. Formally, suppose there are two possible

vaccines. Vaccine 1 with efficacy e1 is available starting at time t1 = 0. Vaccine 2 with efficacy

e2 becomes available at time t2 > 0. Once either vaccine becomes available, it can be produced

at constant rate of δ1 = δ2 = 0.25% of the population daily. We will fix e2 = 95% and analyze a

range of efficacies for vaccine 1, e1 ≤ 95%.

Figure 10 presents results comparing the ratio of burdens averted by the vaccines in simula-

tions. Predictably, the longer the delay in availability of the more-effective vaccine, starting with

the less effective vaccine becomes relatively more beneficial. We find that a delay of two months

or more tips the balance toward immediate use of the less effective vaccine. Although their ex-

act magnitudes depend on assumed parameter values and epidemic scenarios, the results can be

32

1.10

1.07

1.05

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0.69

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0.68

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0.74

0.69

0.66

0.62

0.59

0.57

0.72

0.68

0.64

0.60

0.57

0.56

1.22

1.16

1.10

1.06

1.02

1.00

1.00

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0.90

0.87

0.83

0.82

0.86

0.82

0.78

0.74

0.72

0.70

0.77

0.73

0.70

0.67

0.64

0.63

0.71

0.67

0.64

0.62

0.59

0.58

0.67

0.64

0.61

0.58

0.56

0.55

0.65

0.61

0.58

0.56

0.54

0.53

1.61

1.44

1.29

1.16

1.05

1.00

1.17

1.05

0.94

0.85

0.76

0.73

0.91

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0.36

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0.34

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1.57

1.40

1.24

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1.14

1.02

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0.37

0.64

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0.36

0.64

0.57

0.51

0.45

0.39

0.36

Slow−decrease epidemic Slow−growth epidemic Fast−growth epidemicInfections

Deaths

0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6

0.5

0.6

0.7

0.8

0.9

0.95

0.5

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0.95

Months until 95% effective vaccine available

Effi

cacy

for

the

less

effe

ctiv

e va

ccin

e (e

2)

Less effective better by >5% Comparable (within 5%) 95% effective better by >5%

Figure 10: Burden Averted Using Immediately Available Vaccine Relative to More Effective Vaccine Availablewith Delay. Entries are simulation results for ratio of burden averted using a 95% effective vaccine available afterdelay t2 indicated on horizontal axis, to that from an immediately available vaccine with efficacy e1 indicated on thevertical axis. Entries greater than 1 favor waiting for the 95% effective vaccine, while entries less than 1 favor use ofthe less effective vaccine. Only the situation where it is not feasible to switch to the more effective vaccine later, whenit becomes available, is considered here.

stark. If the immediately available vaccine is 70% effective (comparable to ChAdOx1 nCoV-19

(Oxford/AstraZeneca)) and a 95% effective vaccine is available two months later, then starting vac-

cinations with the immediately available vaccine would reduce infections by 11–22% and deaths

by 20–37%.

If the planner can start with the immediately available vaccine and freely switch to the more

effective vaccine when it becomes available later, switching dominates continuing to use the first

vaccine. Anyone who would have received the immediately available vaccine after time t2 can

be given the more effective vaccine instead, providing more protection. Comparing switching to

waiting for the more effective vaccine requires analysis; being vaccinated with an immediately

33

S E I

D

R

Vaccine 1

P1 N1

Vaccine 2

P2 N2

Figure 11: Compartment Flows in Model with Two Vaccines. Differential equations provided in equations (B10)–(B18) in Appendix B. Additional notes from Figure 2 apply.

available vaccine that is less effective may do little to quell the epidemic and prevents the indi-

viduals from receiving more protection later (unless re-vaccination with a booster shot of a more

effective vaccine is feasible).

Formally, we need to modify the single-vaccine model given by equations (1)–(7) to account

for sequential use of two vaccines. We can do this by adding protected compartments, P1i and

P2i, not-protected compartments, N1i and N2i, vaccination rates, δ1i and δ2i, and vaccine access

indicators v1i(t) and v2i(t) for each of the two vaccines. Differential equations for the model

with two vaccines are provided in equations (B10)–(B18) in Appendix B. Figure 11 provides a

schematic diagram of the compartment flows for the two-vaccine model.

The results are relegated to Figure 15 in Appendix D because they are easy to summarize

in words. The few cases in which delay dominated immediate vaccination in Figure 10 have

disappeared. Starting vaccination immediately and switching later strictly dominates waiting in all

cases with any nontrivial delay period.

34

It is important to acknowledge important limitations. Our analysis has a T = 365 day hori-

zon and is restricted to a single epidemic outbreak, thus abstracting from subsequent epidemic

waves and benefits of reaching herd immunity. We omit these factors in the belief that beyond this

period, it is reasonably likely that additional supply could come online, and policy could be ad-

justed accordingly. Moreover, uncertainty involving booster shots or seasonal vaccination makes a

calculation of longer-term benefits too speculative at this point.

7. Options for Obtaining More Information on the Impact of

Alternative Dosing

As discussed in Section 2, existing immunogenicity data from clinical trials suggest that effec-

tiveness for alternative doses of at least some vaccines could potentially be high (see Figure 1).

Simulations in Section 6.1 show that alternative dosing policies would dramatically reduce mor-

tality and infections if efficacy is at the levels associated with the current data on immunogenicity,

and would still substantially reduce mortality even if efficacy fell significantly, for example to the

level of some existing approved vaccines. However, the evidence of immune response is limited,

and the projected impacts of such policies are subject to model uncertainty and may vary across

vaccines, variants, and epidemic settings.

The high potential benefits, combined with remaining uncertainty, make information on the im-

pact of alternative dosing very valuable. However, despite promising clinical trial data on immuno-

genicity of different doses of COVID-19 vaccines being available since autumn of 2020, we are

aware of only one ongoing immunogenicity trial testing alternative doses: a study of half doses of

mRNA-1273 (Moderna) with 200 participants in Belgium (ClinicalTrials.gov ID NCT04852861),

35

and one real-world evaluation of the impact of alternative dosing on disease burden, recently an-

nounced in Brazil (Governo ES, 2021), which will evaluate immunogenicity and effectiveness of

half a dose of ChAdOx1 nCoV-19 (Oxford/AstraZeneca). For much of this section we discuss

practical options for evaluating alternative dosing policies (which also apply to other dose stretch-

ing policies), most of which could be implemented in a few weeks.

Given recent work in establishing correlates of protection against SARS-CoV-2 infection, fur-

ther immunogenicity trials could provide very valuable information safely and at low cost. While

clinical trial data on a few candidates already exists, much of this is with small sample sizes, and

many more doses could be tested. New immunogenicity trials can be conducted in a matter of

weeks and require only a few hundred participants. Since the outcome measured is not infection,

there is no need to conduct trials in places where the risk of COVID-19 is high—in fact, they can be

conducted in places where the virus is not circulating and which have strong health care systems,

to minimize risk to participants. Clinical pharmacology modeling, routinely used during vaccine

development, should also be used at this stage, allowing us to combine data from multiple trials

and to extrapolate a dose-response function to new doses and across age groups.

Beyond immunogenicity trials, non-randomized approaches can also be used to establish ef-

fectiveness of different dosing strategies against infection or mortality as a vaccination campaign

is rolled out. Observational designs, such as test-negative case-control studies, are recommended

by the WHO to study vaccine effectiveness, and the same methods can be used to quickly de-

termine the effect of alternative dosing in real-world settings. However, unlike immunogenicity

studies, they need to be conducted where infections are occurring.30 Model-based synthesis of

30Both practical and modeling assessments (in influenza) suggest that the risk of bias of these study designs isacceptable (Shi et al. 2017). The number of COVID-19 cases required to detect (with a precision of 10%) 70%efficacy with a test-negative design is 1,345, assuming that vaccine coverage in the underlying population is 50%.This is according to the WHO’s sample size calculator, included in its official guidance document. The number would

36

immunogenicity data, pre-existing clinical trial data (on full doses), and new data on alternative

doses can also be used to extrapolate outcomes between doses, to safely generate estimates for

immunogenicity in high risk individuals, and also to increase statistical power.31

Testing, however, can take time. Even a rapid study of immune response requires, in the

case of 2-dose vaccines, time for administration of two doses (for alternative doses, a minimum

of 3 to 4 weeks apart, depending on the vaccine; for FDF, several months), and at least several

days for immune responses to develop following a second dose. During a period of epidemic

growth, the delay associated with running experiments could be costly in terms of infections and

deaths, and more lives could be saved in expectation by implementing whichever policy has higher

expected value and simultaneously evaluating outcomes. Thus, many countries decided to delay

second doses for some vaccines early on, without waiting for more complete data. In the case

of the UK, the decision was made only weeks into the vaccination campaign. Similarly, data

on alternative dose efficacy was not yet available when the WHO’s Strategic Advisory Group of

Experts on Immunization (SAGE) approved the use of alternative doses of yellow fever vaccine

during epidemics (World Health Organization 2016).

In some cases, randomized trials that explicitly test the impact of dose stretching on infection

and disease risk can also be part of roll-out plans (Kominers and Tabarrok 2020; Bach 2020). Roll-

out of modified plans need not wait until trial results are known. Instead, plans can be adjusted as

new information emerges. The vaccinated can be comprehensively monitored, allowing decision-

makers to modify policy based on infection rates and immune response data.

likely be lower under a non-inferiority design needed for testing alternative doses. Matching techniques can also beused to correct for bias in effectiveness studies (Dagan et al. 2021).

31It is important to note that ChAdOx1 nCoV-19 (Oxford/AstraZeneca) was approved for emergency use in alladults in the UK and Europe despite (at the time) lack of clear evidence on efficacy in the elderly. Extrapolatingresponse across ages for a smaller dose of an already widely used vaccine with comprehensive real-world data is muchless risky than for a new vaccine.

37

An important feature of the dose stretching policies we have analyzed is that they are, to a large

degree, reversible. In the case of FDF, if it is found to be ineffective, the dosing interval can be

shortened. In the case of alternative dosing, reversibility can be understood as the ability to increase

dosing or provide later booster shots of the same or a different vaccine. The costs of reversing

alternative dosing may be higher than those of reversing FDF, since it may require additional

vaccine supply and use of healthcare staff to deliver vaccines. Additionally, if not effective, either

policy will lead to a higher number of infections and deaths in the period until it is reversed.

Even if policymakers are pessimistic about the odds that alternative dosing will be effective,

testing the policy is likely to save lives in expectation as long as there is even a relatively small

chance of success. Suppose there is a 75% chance that half-dose efficacy is 30% and a 25% chance

that it is 90%. If the policy is reversible, trying alternative dosing with a limited population to learn

whether efficacy was truly 30% or 90% would save lives in expectation. If the trial was done in a

healthy volunteer population in a region with access to good care, health risks would be minimal,

and tiny relative to the potentially enormous gains from rapidly increasing vaccination rates with

alternative dosing, as long as efficacy could be learned quickly enough.

Ultimately, regulators and public health officials in each jurisdiction have to decide whether to

wait for additional immunogenicity studies before testing efficacy of alternative doses, and, if they

do test alternative dosing, whether to do so as part of vaccine roll-outs or through formal trials.

8. Conclusion

The COVID-19 vaccination rate in most countries is limited by scarce vaccine supplies. We an-

alyze policies that stretch scarce supplies, speeding protection to more people. In particular, we

38

explore the impacts of three dose stretching policies: alternative dosing; delaying second doses;

and using available vaccines early rather than waiting for more efficacious vaccines. Delayed sec-

ond doses has been tested as part of vaccination roll-outs in some countries, with indications of

substantial benefits for at least some vaccine-variant combinations. However, alternative dosing

has not been tested yet, despite high immunogenicity from smaller doses of vaccines observed in

early stage clinical trials. For alternative doses, we use the high correlation (across vaccines) be-

tween neutralizing antibody response and efficacy against disease to provide suggestive evidence

that half or even quarter doses of some vaccines generate immune responses associated with high

efficacy. Next, we used an SEIR model to explore the impact of the three dose stretching ap-

proaches on disease burden, and show that all three substantially reduce infections and mortality

over a wide range of plausible efficacy levels. These results derive from the value of speed in

vaccinations — both starting vaccinations early and vaccinating at high daily rates. The value is

so high that under supply constraints, the gains from enhanced speed enabled by dose stretching

outstrip the costs of potential efficacy loss for a wide range of efficacies for stretched doses.

Our simulations used averted burden of infection and death as outcome variables, abstracting

from other important economic and social costs. Faster vaccination could substantially reduce the

time until relaxation of lockdowns and other costly non-pharmaceutical interventions. alternative

dosing, in particular, can also bring long-term benefits, even if supply constraints are eventually

alleviated, such as a decrease in production costs for vaccine manufacturers and lower prices for

consumers. Additionally, the trials and testing required to evaluate and potentially implement

alternative dosing could also be helpful in the continued development of newer vaccine platforms,

such as viral vector and mRNA vaccines, since little is currently known about optimal dosing

for such vaccines. Our simulations thus likely underestimate the wider benefits of accelerating

39

vaccination with dose-stretching policies.

To accommodate uncertainty about the efficacy of untested alternative dosing policies, our

analytical approach was to simulate a range of potential values for the efficacy loss entailed by

the policy. In practice, policymakers may not know which of these efficacy values applies to their

situation. However, it is possible to learn more safely, quickly, and inexpensively: the reversibility

of the dose-stretching policies strengthens the case for trying them. If efficacy falls too much,

the standard dose policy can be reinstated; if not, the dose-stretching policy can be retained and

expanded.

Dose stretching may be particularly beneficial for low-income countries (LICs), not necessarily

through their use in LICs themselves but dose-stretching in other countries could free up supplies

to start widespread vaccination in LICs earlier. LICs have signed fewer bilateral deals with vaccine

manufacturers and have received small allocations from COVAX and other international arrange-

ments. If the present capacity is used without stretching measures, it may take years before LICs

reach 70% coverage of COVID-19 vaccines (Castillo et al. 2021). Estimating the benefit to LICs of

having other countries undertake stretching measures is beyond the scope of this paper. Instead, we

discuss dose stretching in LICs in Appendix C, which repeats the main simulations, parametrized

for LICs.

Dose stretching may also be particularly beneficial for non-elderly populations, who often

have stronger immune responses to vaccines. Decision-makers might consider rolling out dose

stretching policies only for younger adults, the majority of whom remain unvaccinated by the end

of May 2021, including in many high income countries. For COVID-19 vaccines, this may also

reduce side effects (including mild to moderate ones that can still be a barrier to uptake), which

have generally been higher in non-elderly populations.

40

Our SEIR model is based on a vaccine with 95% efficacy and does not allow for partial pro-

tection (e.g., from mortality but not infection). It uses an age structure similar to those in many

high income countries and a disease burden appropriate for SARS-CoV2 variants most prevalent

in 2020. In further research, we will modify some of the modeling assumptions. In particular, we

will examine the case of a vaccine with efficacy in the 70% range (such as for ChAdOx1 nCoV-19

(Oxford/AstraZeneca), or mRNA vaccines against recently emerged variants), explore the case of

low-income countries in more detail, allow for differences in effectiveness against different types

of disease burden, and check fo r robustness of our conclusions to the emergence of viral vari-

ants. Further work should also investigate the effect that simultaneously implementing alternative

dosing and increased delays between two doses would have on health benefits. Additionally, in

future work we plan to consider longer time horizons, accommodating boosters, loss of immu-

nity, and endogenous behavioral response to risk, such that R = 1 for an extended period of time

(Gans 2020). We will also explicitly model a global production constraint, not only the problems

of individual countries, and will analyze scenarios where it is not possible to maintain strict age

prioritization. Last, we will extend the analysis to allow for the vaccination of children.

To conclude, we argue that alternative COVID-19 vaccine dosing regimens could potentially

dramatically accelerate global vaccination and reduce mortality, and that these potential benefits

dwarf the costs of testing these regimens. While our paper focuses on the COVID-19 context, its

conclusions are broadly applicable to vaccine shortages during an epidemic.

41

Appendix A: Survey of Evidence on Dose StretchingThis appendix surveys existing evidence from medical literature on the effects on individual vac-cine efficacy (VE) of dose stretching policies. Table 1 lists clinical trials for several impor-tant vaccines. Note that in some cases, while early trials tested multiple doses, later trials usedonly a single dose size (such as for BNT162b2), while in others (e.g., ChAdOx1 nCoV-19 (Ox-ford/AstraZeneca)), multiple dose sizes were tested at all stages.

Alternative DosingIn early stage clinical trials, lower dosages of COVID-19 vaccines were often found to stimulatea strong NAb response, at least in non-elderly patients. Evidence on the immunogenicity of arange of dose sizes of each vaccine is summarized in Table 2. Note that in some later trials, suchas those for JNJ-78436735 (Johnson & Johnson) and NVX-CoV2373 (Novavax), Phase 3 clinicaltrials proceeded with the smaller of two dose options tested in early trials after those trials foundno statistically significant difference in immune response between the doses.

42

43Vaccine Phase Date posted 1st

dosere-sults*

Doses Doseinterval

(days)

Treatment arms Agegroup

N Clinicaltrials.govnumber

ChAdOx1nCoV-19

1/2 3/27/2020 Yes 2 28, 56 • 1× 5e10 v.p.• 2× 5e10• 5e10, 2.2e10• 5e10, 3.5-6.5e10

18-55 1090 NCT04324606

1/2 6/23/2020 No 2 28 2× 5-7.5e10 v.p. 18-65 2130 NCT04444674

2/3 5/26/2020 Yes 2 28-42 • 1× 5e10 v.p.• 2× 3.5-6.5e10• 5e10, 2.2e10• 5e10, 3.5-6.5e10

18-70+ 12390 NCT04400838

3 9/2/2020 Yes 2 28-84 • 1× 5e10 v.p.• 5-10, 3.5-6.5e10

18+ 10300 NCT04536051

JNJ-78436735

1 6/18/2020 Yes 1 n/a • 1× 5e10 v.p.• 1× 1e11

18-55 25 NCT04436276

1/2a 6/18/2020 Yes 2 56 • 1× 5e10 v.p.• 2× 5e10• 1× 1e11• 2× 1e11

18-55,65+

1085 NCT04436276

3 8/10/2020 Yes 1 n/a 1× 5e10 v.p. 18+ 44325 NCT04505722

mRNA-1273

1 2/25/2020 No 2 28 • 2× 25µg• 2× 50• 2× 100• 2× 250

18+ 120 NCT04283461

2a 5/28/2020 No 2 28 • 2× 50µg• 2× 100

18+ 660 NCT04405076

NVX-CoV2373**

1/2 4/30/2020 Yes 2 21 • 2× 5µg• 2× 25• 5, 25

18-59/18-84

131/1500

NCT04368988

BNT162b21 4/20/2020 No 2 21 • 2× 10µg

• 2× 20• 2× 30• 2× 100

18-55,65-85

195 NCT04368728

2/3 4/20/2020 No 2 21 30µg 12-15,16-55,55+

43548 NCT04368728

Table 1: *Trial reports immunogenicity at least three weeks after dose administration, before a second dose (ifplanned) has been administered, and has a comparable outcome (in terms of age group, dose, and day measured)for second doses. **Treatment arms also included groups in which each vaccine dose arm was administered with andwithout 50µg of Matrix-M adjuvant.

44

Vacc

ine

nAb

assa

yD

ay of2n

ddo

se

Age

grou

pN

Mea

-su

red

on day

Stan

-da

rddo

se*

Dos

ete

sted

Dos

efr

ac-

tion

NA

b re-

spon

se

Stan

dard

dose

NA

bre

spon

se

NA

bre

spon

seas

frac

tion of

stan

dard

dose

Diff

eren

ceis si

gnifi

cant

(at5

%le

vel)?

ChA

dOx1

nCoV

-19

MN

8014

18-5

541

425e

10v.

p.2.

2e10

v.p.

0.44

161

193

0.83

no

56-6

928

420.

4414

314

40.

99no

70+

3442

0.44

150

161

0.93

no

BB

V15

2PR

NT

5028

12-6

519

056

6µg

3µg

0.5

100

197

0.51

yes

JNJ-

7843

6735

PRN

TIC

50n/

a18

-55

2456

5e10

v.p.

1e11

v.p.

231

028

81.

08no

65+

5028

221

227

70.

77no

mR

NA

-127

3

PRN

T80

28

18-5

515

42

100µ

g

25µg

0.25

340

640

0.52

no

MN

5018

-55

7842

50µg

0.5

1733

1909

0.91

no

55+

6342

50µg

0.5

1827

1686

1.08

no

NV

X-

CoV

2373

**M

NIC

>99

2118

-59

5035

5µg

25µg

533

0539

060.

85no

BN

T16

2b2*

**PR

NT

5021

18-5

512

28

30µg

10µg

0.33

157

361

0.43

n/a

65-8

512

3510

µg0.

3311

120

60.

54n/

a

18-5

512

2820

µg0.

6736

336

11.

01n/

a

65-8

512

2820

µg0.

6784

206

0.41

n/a

Tabl

e2:

Neu

tral

izin

gan

tibod

y(n

Ab)

resp

onse

slis

ted

are

the

peak

leve

lsre

cord

edin

publ

ishe

dtr

iald

ata.

Sour

ces:

Ram

asam

yet

al.

2020

(ChA

dOx1

nCoV

-19,

Oxf

ord/

Ast

raZ

enec

a),E

llaet

al.

2021

(BB

V15

2,C

ovax

in),

Sado

ffet

al.

2021

a(J

NJ-

7843

6735

,Jo

hnso

n&

John

son)

,Ja

ckso

net

al.

2021

(mR

NA

-127

3,M

oder

na-

25µg

),C

huet

al.

2021

(mR

NA

-127

3,M

oder

na-5

0µg)

,Kee

chet

al.2

020

(NV

X-C

oV23

73,N

ovav

ax),

Wal

shet

al.2

020

(BN

T16

2b2,

Pfize

r).

*“St

anda

rddo

se”

isw

hati

sbe

ing

used

inva

ccin

ero

ll-ou

tsth

usfa

r(v.

p.=v

iral

part

icle

s).

**B

oth

dose

sw

ere

adm

inis

tere

dto

geth

erw

ith50

µgof

adju

vant

.***

Sam

ple

size

was

too

smal

lto

dete

rmin

esi

gnifi

canc

e.

First Doses FirstThere is already some evidence both from clinical trials and real-world data on the efficacy of firstdoses. Efficacy varies by vaccine, by dose size, and by the virus variant. In some cases, first doseshave been found to be highly effective.

• Efficacy of ChAdOx1 nCoV-19 after two doses was 62-90 percent (Voysey et al. 2021).Efficacy at preventing symptomatic infection was 73 percent starting 22 days after the firstdose (UK Joint Committee on Vaccination and Immunisation 2020a). A recent clinical trialdemonstrated that delaying the second dose of ChAdOx1 nCoV-19 (Oxford/AstraZeneca)to 12 weeks or later improved long-term vaccine efficacy (Voysey, et al. 2021). Hence theauthors concluded, “ChAdOx1 nCoV-19 vaccination programs aimed at vaccinating a largeproportion of the population with a single dose, with a second dose given after a 3 monthperiod is an effective strategy for reducing disease, and may be the optimal for rollout of apandemic vaccine when supplies are limited in the short term.”

• In Phase 3 clinical trials, VE of BNT162b2 (Pfizer) between 15 and 28 days after the firstdose (before immune response from the second dose, delivered at 14 days, would have kickedin) was 90% (CITE).32

• In a trial that administered first and second doses of mRNA-1273 (Moderna) four weeksapart, VE two weeks after the first dose was 95.2% (Baden et al. 2020).

While we have limited information on how long these immune responses last, we do knowthat the second doses of mRNA-1273 (Moderna) were given as late as 42 days after the first shot(Infectious Disease Society of America 2021), that the UK’s Joint Committee on Vaccination andImmunisation’s analysis suggests that protection from ChAdOx1 nCoV-19 (Oxford/AstraZeneca)lasts up to 3 months (JCVI 2020a), and that immunity from natural infection seems to last at least6 months.

Most vaccine schedules offer some flexibility on when booster shots may be taken, and typi-cally require a minimum interval of over four weeks between shots.

Real world data on ongoing vaccinations has produced results similar to those found in clinicaltrials.

• In Israel, BNT162b2 (Pfizer) was estimated to be 78% effective against hospitalizations and80% effective against disease 21-27 days following the first dose (Dagan et al. 2021).

• A study of data covering the entire population of Scotland found that BNT162b2 and ChA-dOx1 nCoV-19 (Oxford/AstraZeneca) reduced hospitalization after four weeks by 85 and 94percent, respectively, in real-time vaccination campaigns (University of Edinburgh 2021).

• A study of older adults in the UK found that a single dose of BNT162b2 or ChAdOx1 nCoV-19 was 80% effective at preventing hospitalization (Lopez Bernal et al. 2021a).

32One trial found that first dose efficacy was only 54%, but most infections in the treatment group occurred in thefirst two weeks, before the immune response is likely to have kicked in.

45

• In the UK, a study of healthcare workers who received the first dose of BNT162b2 foundthat it was 75% effective at preventing positive cases and reduced asymptomatic infectionsby half (Hall et al. 2021).

However, first doses might not be as effective for all vaccines. For example, the first dose ofCoronaVac was found to be only 3% effective in a study of Chile’s vaccine rollout (although trialshave also found CoronaVac to be less effective than other vaccines even after two doses) (Dyer2021). It is possible that the coronavirus outbreak in Chile in April was amplified by CoronaVac’slow first-dose efficacy, which made up 93% of administered doses (over a third of adults hadreceived at least the first dose of the vaccine at the beginning of the month) (Taylor 2021).

First doses have also been less effective against new variants of the COVID-19 virus.33.

• First doses of BNT162b2 (Pfizer) were only 17% effective against the South African variant,B.1.351 (Burn-Murdoch et al. 2021).34

• Data from the UK suggest that first doses of BNT162b2 and ChAdOx1 nCoV-19 (Ox-ford/AstraZeneca) are only 51% effective against the B.1.17 variant (Lopez Bernal et al.2021b).35

• New data from India, aggregated across BNT162b2 and ChAdOx1 nCoV-19, suggests firstdose efficacy against the B.1.617.2 variant is just 33% (Lopez Bernal et al. 2021b).36

Immune escape riskOne serious concern about modified vaccination approaches is that they might lead to weak im-mune responses and immune escape through mutation (Wadman 2021). In considering such risksit is important to also consider the risks of the status quo. Without a modified vaccination approachthere is a higher probability of more infections. A non-vaccinated person who becomes infectedgoes through a period of “partial immunity” and thus also increases the risk of immune escape.Indeed, variants of the SARS-CoV-2 virus are already circulating that are more transmissible andmight be less vulnerable to vaccines but these arose before widespread vaccination (Kupferschmidt2021). Thus, it isn’t clear whether the balance of probabilities on immune escape favors or dis-favors the modified approach. The risk of immune escape should also be evaluated in the largercontext of vaccine approval. In June 2020, the FDA was willing to accept a vaccine with an ef-ficacy rate as low as 50%37 even given the risks of immune escape. A vaccine efficacy rate of

33JNJ-78436735 (Johnson & Johnson), which is administered as a single dose, was somewhat less effective againstthe South African variant, but still exceeded WHO standard levels, with 52% and 64% efficacy 14 days and 28 daysafter the shot, respectively (Sadoff et al. 2021b)

34Second doses were 75% effective.35Second dose VE is also lower, although not as much: 66% and 93% for ChAdOx1 nCoV-19 and BNT162b2,

respectively.36Second dose VE was 60% and 88% for ChAdOx1 nCoV-19 and BNT162b2, respectively.37“To ensure that a widely deployed COVID-19 vaccine is effective, the primary efficacy endpoint point estimate

for a placebo-controlled efficacy trial should be at least 50%” (U.S. Food and Drug Administration 2020a).

46

70%38 is very good. If the efficacy rate of a dosage regime, such as offering a second dose of anmRNA vaccine at 12 weeks never falls below 70%, then the dosing regime should be consideredno more risky than the approvable vaccine. The calculus should also take into account the fact thatwe have some indication that vaccines may be protective against asymptomatic infection even withone dose (e.g. (Voysey et al. 2021)) and that milder and less symptomatic infections lead to lesstransmission (Kampen et al. 2020).

The New and Emerging Respiratory Virus Threats Advisory Group (NERVTAG), a scientificadvisory group to the British government, recently considered the risk of immune escape andconcluded that although the risk of immune escape from delaying a second dose is real it is likelysmall, especially in comparison to other sources of immune escape such as therapeutics and naturalinfection. Moreover, the risk is outweighed by the measurable benefits of getting more does outquickly.

It is not currently possible to quantify the probability of emergence of vaccineresistance as a result of the delayed second dose, but it is likely to be small.The UKcurrently has more than 1,000 COVID-19 related deaths each day and has limitedsupplies of vaccine. In the current UK circumstances the unquantifiable but likelysmall probability of the delayed second dose generating a vaccine escape mutant mustbe weighed against the measurable benefits of doubling the speed with which the mostvulnerable can be given vaccine-induced protection.

...a single dose of vaccine does not generate a new/novel risk. Given what wehave observed recently with the variants B.1.1.7 and B1.351, it is a realistic possibilitythat over time immune escape variants will emerge, most likely driven by increasingpopulation immunity following natural infection.

38A recent study (Bartsch et al. 2020) suggested that a vaccine of efficacy 70 percent could prevent a COVID-19epidemic from taking off, and one of 80 percent could extinguish an epidemic without any other measures such associal distancing.

47

Appendix B: Extensions of Epidemiological ModelSimulating several policies required extending the basic epidemiological model in (1)–(7). Thisappendix presents the systems of differential equations behind those extensions.

B1: Model with Two Doses of a Single VaccineThe analysis of a first-doses-first (FDF) policy in Section 6.2 requires extending the basic model toallow one or two doses to have differing efficacy and to connect the delay between doses to the rateof vaccination. The model maintain the assumption that a single vaccine candidate is available. Inthis subsection, let subscripts 1 and 2, respectively indicate variables associated with the first andsecond doses. The following differential equations govern the extended model:

Si(t) =−λi(t)Si(t)− vi(t)δ1iSi(t) (B1)Ei(t) = λi(t)[Si(t)+N1i(t)+N2i(t)]− γ

′Ei(t) (B2)Ii(t) = γ

′Ei(t)− γ′′Ii(t) (B3)

Di(t) = piγ′′Ii(t) (B4)

Ri(t) = (1− pi)γ′′Ii(t)− vi(t)δ1iRi(t) (B5)

P1i(t) = vi(t)δ1i[e1Si(t)+Ri(t)

]− vi(t)δ2iP1i(t) (B6)

P2i(t) = vi(t)δ2ie2[P1i(t)+N1i(t)] (B7)

N1i(t) = vi(t)δ1i(1− e1)Si(t)− vi(t)δ2iN1i(t)−λi(t)N1i(t) (B8)N2i(t) = vi(t)δ2i(1− e2)[P1i(t)+N1i(t)]−λi(t)N2i(t). (B9)

B2: Model with Two VaccinesThe basic model must be extended if the planner is allowed to switch to the more effective vaccinewhen it becomes available because the first vaccine continues to provide protection to the success-fully immunized when the new vaccine is introduced, governed by different parameters. In thissubsection, we reinterpret subscript 1 as indicating variables associated with the less effective vac-cine available earlier and 2 as indicating prime variables associated with the more effective vaccineavailable later. Compartment flows follow these differential equations:

Si(t) =−λi(t)Si(t)− [v1i(t)δ1i + v2i(t)δ2i]Si(t) (B10)Ei(t) = λi(t)[Si(t)+N1i(t)+N2i(t)]− γ

′Ei(t) (B11)Ii(t) = γ

′Ei(t)− γ′′Ii(t) (B12)

Di(t) = piγ′′Ii(t) (B13)

Ri(t) = (1− pi)γ′′Ii(t)− [v1i(t)δ1i + v2i(t)δ2i]Ri(t) (B14)

P1i(t) = v1i(t)δ1i[e1Si(t)+ Ri(t)

](B15)

P2i(t) = v2i(t)δ2i[e2Si(t)+ Ri(t)

](B16)

N1i(t) = v1i(t)δ1i(1− e1)Si(t)−λi(t)N2i(t) (B17)

N2i(t) = v2i(t)δ2i(1− e2)Si(t)−λi(t)N1i(t). (B18)

48

Appendix C: Low-Income Countries

The simulations so far have been calibrated based on data from a subset of countries with the mostextensive data, typically high-income country (HIC) parameters. These differ in several respectsfrom parameters for low-income countries. LICs generally have much younger populations. Ad-ditionally, mortality risk rises less steeply with age in LICs than HICs, close to a two-fold increaseper decade (Demombynes 2020) compared to the three-fold increase per decade in HICs. Otherfactors also differ, including the virus variants that are most frequently found in both areas andthe behavioral aspect of the population (for example, for a significant portion of the population inLICs, self-isolation might be infeasible). Patterns may also be changing over time, as exemplifiedby India’s terrible recent (April 2021) wave of infections. Our current analysis abstracts from thisand should be considered preliminary.

Infections Deaths

2.00

1.00

0.75

0.50

0.25

0.10

2.00

1.00

0.75

0.50

0.25

0.10

0

25

50

75

100

0

25

50

75

100

Percentage of population vaccinated daily

% b

urde

n av

erte

d

Supply constraint HIC LIC Epidemic scenario Slow−decrease Slow−growth Fast−growth

Figure 12: Comparing Averted Burden from Faster Vaccination in LICs to HICs. Vertical axis shows percentagereduction in burdens relative to no vaccination, in infections (left panel) and deaths (right panel), at various vaccinationspeeds (horizontal axis) and epidemic scenarios (colors). The plot is analogous to Figure 4 but with low-incomecountry added (dashed lines) to high-income country case (solid lines).

Figure 12 reprises the results for burden averted by faster vaccination for LICs that were pro-vided for HICs in Figure 4. The broad pattern of results is similar for LICs and HICs. For bothsets of countries, faster vaccination has a large and nonlinear effect on the proportion of diseaseburden without a vaccine averted. At high vaccination rates (1–2% per day), then burden reduc-tions in LICs are very similar to HICs. At very low vaccination rates, the percentage of burdenaverted is substantially larger in LICs than HICs. For example, at a vaccination rate of 0.1% of

49

the population per day under the slow-growth scenario, 19% of cases are averted in HICs but 54%in LICs. The difference is likely due to population structure. Only 5% of the LIC population isabove age 60 compared to 25% of the population in HICs. An increase in a very low vaccinationrate allows LICs to quickly move beyond their senior populations to younger cohorts with highertransmission rates. The quantitative results depend on our assumption, in the absence of good dataon the contact matrix for LICs, that social mixing is the same in LICs as HICs.

We reprized all of the previous HIC results for LICs but for brevity present just the results onthe relative benefits of alternative dosing, in Figure 17 in Appendix D. The relative benefit of agiven alternative-dosing policy shown for LICs is slightly lower than that for HICs in Figure 6, butthe magnitudes are similar.

Appendix D: Supplementary Exhibits

50

51

Table 3: Parameters Specified in Epidemiological Model

Parameter Interpretation Value Comments

T Length of each simu-lation (in days)

365

ni Age distribution overdifferent age groups:high income and lowincome countries

[0,10): 0.11, 0.29[10,20): 0.11, 0.23[20,30): 0.13, 0.17[30,40): 0.14, 0.12[40,50): 0.14, 0.08[50,60): 0.13, 0.05[60,70): 0.11, 0.03[70,80): 0.08, 0.02[80,∞): 0.05, 0.004

World Population Prospects 2019 distribution forhigh and low income country categories, based onR package wpp2019.

c(i, j) Contacts from age co-hort i to age cohort j

9x9 matrix based onlarge scale survey ofage-structured contacts

Mossong et al. (2008).Dominant eigenvalue is y = 14.17.

q Probability of trans-mission on contact

0.0203 for R=0.99,0.02264 for R=1.10.0411 for R=2

Adjusted to match desired R0.

γ ′ Reciprocal of averagelength of incubationperiod

1/5 = 0.2 Incubation period was initially estimated to beabout five days (Verity et al. 2020; Cevik et al.2021). Some have suggested a longer period, butwe opted for five days to account for shorter serialinterval for COVID-19 (five to six days), as we donot model pre-sympotmatic transmission.

γ ′′ Reciprocal of averagelength of infectiousperiod

1/5 = 0.2 While duration of viral shedding is longer, infec-tiousness decreases quickly after onset of symp-toms (Cevik et al. 2021).

pi Age-specific infectionfatality rate (IFR)

[0,10): 2e-05[10,20): 6e-05[20,30): 3e-04[30,40): 8e-04[40,50): 0.0015[50,60): 0.006[60,70): 0.022[70,80): 0.051[80,∞): 0.093

Based on a recent meta-analysis of IFRs (Man-heim et al. 2020).

52

Vaccinated Currently infected Susceptible

Jan Apr Jul Oct Jan Apr Jul Oct Jan Apr Jul Oct

20

40

60

80

0

0.1

0.2

0.3

0

20

40

60

80

time

% o

f age

coh

ort

Age cohort

80+

[70,80)

[60,70)

[50,60)

[40,50)

[30,40)

[20,30)

[10,20)

[0,10)

Figure 13: Age-specific Evolution of Vaccinated, Infected, and Susceptible Compartments. Colors indicate com-partment percentages for various age cohorts. Assumes slow-growth epidemic scenario and baseline values of param-eters (95% efficacy, vaccination rate of 0.25% of population per day, target 80% vaccination rate in cohorts age 20 andover). The assumed policy of prioritizing older cohorts is reflected in vaccination panel. Because they are vaccinatedearlier, older cohorts experience an earlier downturn from their peak infection rate.

53

1.45 1.40 1.50 1.65 1.85 4.00

1.30 1.30 1.35 1.40 1.50 2.05

1.20 1.20 1.20 1.25 1.30 1.50

1.15 1.10 1.10 1.15 1.15 1.25

1.05 1.05 1.05 1.05 1.05 1.10

1.00 1.00 1.00 1.00 1.00 1.00

2.10 2.40 3.50 4.50 7.50 Inf

1.75 1.90 2.15 2.55 3.50 10.00

1.45 1.55 1.65 1.80 2.00 3.50

1.25 1.30 1.35 1.40 1.45 1.75

1.10 1.10 1.10 1.15 1.15 1.20

1.00 1.00 1.00 1.00 1.00 1.00

1.40 1.40 1.55 1.75 2.05 7.50

1.30 1.30 1.35 1.45 1.55 2.40

1.20 1.20 1.20 1.25 1.30 1.60

1.10 1.10 1.10 1.15 1.15 1.25

1.05 1.05 1.05 1.05 1.05 1.10

1.00 1.00 1.00 1.00 1.00 1.00

2.10 2.30 3.50 5.00 11.00 Inf

1.75 1.85 2.15 2.65 3.50 18.00

1.45 1.55 1.65 1.85 2.05 3.50

1.25 1.30 1.35 1.40 1.45 1.80

1.10 1.10 1.10 1.15 1.15 1.20

1.00 1.00 1.00 1.00 1.00 1.00

1.70 1.60 1.60 Inf Inf Inf

1.50 1.40 1.35 1.70 Inf Inf

1.30 1.25 1.25 1.30 1.95 Inf

1.20 1.15 1.15 1.15 1.25 Inf

1.05 1.05 1.05 1.05 1.10 1.35

1.00 1.00 1.00 1.00 1.00 1.00

2.50 4.00 Inf Inf Inf Inf

1.85 2.55 4.50 Inf Inf Inf

1.50 1.90 1.90 4.00 Inf Inf

1.25 1.45 1.45 1.50 2.05 Inf

1.10 1.15 1.15 1.15 1.20 1.85

1.00 1.00 1.00 1.00 1.00 1.00

Slow−decrease epidemic Slow−growth epidemic Fast−growth epidemic

InfectionsD

eaths

0.10

0.25

0.50

0.75

1.00

2.00

0.10

0.25

0.50

0.75

1.00

2.00

0.10

0.25

0.50

0.75

1.00

2.00

0.5

0.6

0.7

0.8

0.9

0.95

0.5

0.6

0.7

0.8

0.9

0.95

Baseline percentage of pop. vaccinated daily

Effi

cacy

of f

ract

iona

l dos

e

Figure 14: Threshold Speed-up at which Alternative Dominates Full Dosing. Entries present threshold speed-upin the vaccination rate when moving from alternative to full dosing such that alternative dosing averts greater diseaseburden. Shading intensity increases with the needed threshold. Entries marked “Inf,” denoting infinity, are cases inwhich full dosing dominates for all speed-ups simulated, even as high as 32. Reciprocal of entry can be interpreted asthe size of alternative dose, holding constant efficacy on vertical axis, below which alternative dominates full dosing.Each tile represents a different combination of epidemic growth, level of efficacy of alternative dose, and vaccinationrate assumed for the full dose. Maintains baseline assumption that full dose is 95% effective.

54

0.91

0.91

0.91

0.90

0.90

0.89

0.87

0.86

0.85

0.84

0.84

0.83

0.85

0.83

0.82

0.81

0.80

0.79

0.83

0.82

0.80

0.79

0.77

0.77

0.82

0.81

0.79

0.77

0.76

0.75

0.82

0.80

0.78

0.76

0.75

0.74

0.92

0.89

0.87

0.84

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Figure 15: Burden Averted Using Delayed Vaccine Relative to Switching Policy. Entries are ratios of burdenaverted using vaccine 2, a 95% effective vaccine available after delay t2 indicated on horizontal axis, to that fromstarting with vaccine 1, with efficacy e1 indicated on the vertical axis, immediately and switching to vaccine 2 at t2.Entries greater than 1 favor vaccine 2 and less than 1 favor the switching policy. The policies are no different whenthere is no delay, both equivalent to using the more-effective vaccine only.

55Second−dose delay policy: SDF HDF−60 FDF

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Figure 16: Burden Averted Relative to No Vaccination under Various Delays in Second Dose. Results relatedto the same policies studied in Figure 9, but here burden that each policy averts is compared to no vaccination, whileFigure 9 compares SDF to the optimal alternative. SDF refers to second doses first, the status-quo policy of delayingfour weeks until the second dose; FDF refers to first doses first, delaying 12 weeks until the second dose; and HDF-60refers to a hybrid policy of delaying four weeks for age 60 and over and 12 weeks for under 60.

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Figure 17: Comparing Full to Alternative Dosing in LICs. Repeats simulation results from Figure 6 on the therelative burden of infections (top panel) and deaths (bottom panel) under alternative dosing vs full dose but uses LICrather than HIC parameters for the size (ni) and mortality rate (pi) in age cohorts. Values lower than 1 favour alternativedose. Contact matrix and other parameters are the same as in the HIC case. See Figure 6 for additional notes.

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